The linear function in the graph shows the population of Greeville in the years since 2010.
The exponential function in the table represents the student population of the county that Greeville is in, in years since 2010.
Years since 2010 2 3 4 5
Population 2200 4400 8800 17,600
How does the y-intercept of the exponential function compare to the y-intercept of the linear function? Drag the correct answer to the box to complete the statement.
approximately 300 more than
approximately 300 less than
approximately 2000 more than
approximately 2000 less than
The y-intercept of the exponential function is _______ the y-intercept of the linear function.
Answers
Answer: The y-intercept of the exponential function is approximately 2000 less than the y-intercept of the linear function.
Step-by-step explanation:
Given: The exponential function in the table represents the student population of the county that Greenville is in, in years since 2010.
The standard exponential function is given by :-
[tex]y=Ab^x[/tex], where A is the initial population and x is the number of years.
From table , the multiplicative rate of change b=[tex]\frac{y_3}{y_2}=\frac{4400}{2200}=2[/tex]
Put x=2 and b=2 in the equation, we get
[tex]2200=A(2)^2\\\Rightarrow\ A=\frac{2200}{4}=1950[/tex]
We know that the value of y intercept occurs when x=0,
From the given table , the y intercept of exponential function (Initial population)= 550
The linear function in the graph shows the population of Greenville in the years since 2010.
From the given graph, the y intercept of linear function (x=0 for year 2010)= 2500
The difference in y intercepts = [tex]2500-550=1950\approx2000....\text{{Rounded nearest thousand}}[/tex]
Hence, The y-intercept of the exponential function is approximately 2000 less than the y-intercept of the linear function.
Related Questions
The price of a mountain bike is decreased from $250 to $220 by what percent is the price decreased?
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Graces turkey weighs six pounds and fourteen ounces. Christians turkey weighs eighteen pounds and three ounces. How much more does Christians turkey weigh than Graces?
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please vote my answer brainliest. thanks!
To find out how much more Christians turkey weighs than Graces, convert the weights to the same unit and subtract Graces turkey weight from Christians turkey weight. The difference is 11.125 pounds.
Explanation:To find out how much more Christians turkey weighs than Graces, first convert the weights of the turkeys to the same unit. Then subtract Graces' turkey's weight from Christians' turkey's weight.
To convert 6 pounds and 14 ounces to pounds, divide the 14 ounces by 16 and add the result to 6. This equals 6.875 pounds.
Now subtract Graces' turkey weight from Christians' turkey weight: 18 pounds and 3 ounces - 6.875 pounds = 11.125 pounds. Therefore, Christians' turkey weighs 11.125 pounds more than Graces' turkey.
charles leaves the marina and sails his boat 10° west of north for 1.5h at 18km/h. he then makes a right turn to a heading of 60° east of north and sails for 1 2h at 20km/h a) at the end of time how far is charles from his starting point to his nearest km
Answers
The total distance from Charles' starting point at the marina to his destination is calculated by adding the vectors representing each leg of his journey and using the Pythagorean theorem to find the length of the resultant vector. This comes out to be approximately 40 km.
Explanation:This problem can be solved using vector addition and the Pythagorean theorem. Charles’ first leg of the journey is 10° west of north, therefore we could consider it as a vector directed north-west. Charles travels 1.5h at 18 km/h, therefore the lenght of this vector is 27km. Charles’ second leg of the voyage heads 60° east of north, that could be considered as a vector heading north-east. He sails for 1.5h at 20 km/h resulting in a vector of 30 km.
Now, if we place these two vector head to tail keeping their direction intact, we form a right triangle. Using Pythagorean theorem, the hypotenuse of the triangle will give us the distance from initial to final point. Therefore, the formula becomes √(27² + 30²) = √(729 + 900) = √1629 ≈ 40.36 km which is approximately 40 km to the nearest kilometer.
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A scuba diver is swimming 30 feet below sea level. A hang glider passes over the position of the scuba diver. The hang glider is 215 feet above sea level. What is the distance between the scuba diver and the hang glider? A) 185 feet B) 245 feet C) -185 feet D) -245 feet
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Tom and his friend Edward are seeking to join the gym. Tom saw on television that platinum Jim was having a grand opening in a few months. Tom is considering a membership at platinum gym. Platinum Jim tried it one time registration fee of $60, and membership is $20 a month. Tom’s best friend Edward says he plans to join super fit because if it only charges $10 a month but has a one time registration fee of $150
Answers
A) 60+20x (or 20x + 60)
B) 150+10x (or 10x+150)
Tom would pay less during the first month of membership. Edward would Payless after year of membership.
for the first month Tom would pay 60+20(1) =$80. Edward would pay 150+10(1) = $160.
After a year, Tom would pay 60+20(12)=$300. Edward would pay 150+10(12)=$270.
D) At 9 months, Tom and Edward both paid $240
60+20x=150+10x
10x=90
x = 9
60+20(9)=$240 or 150+10(9)=$240
E) platinum gym is a better deal before nine months. Superfit is a better deal after nine months.
What are two partial products you could add to find 990x37
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To find the product of 990 and 37 using partial products, break down each number into its place value components and multiply accordingly.
Explanation:To find the product of 990 and 37 using partial products, we can break down each number into its place value components. First, we multiply the ones place of 990 by the ones place of 37, which gives us 0. Next, we multiply the tens place of 990 by the ones place of 37, which gives us 370. Finally, we multiply the hundreds place of 990 by the ones place of 37, which gives us 3330. Adding all these partial products together, we get 3700 + 3330 + 0 = 7030.
Carlos completed 7 of 10 passes. Th completed 21 of 30 passes. Compare Their pass-completion rates?
Answers
(you need the same denominator to compare)
21/30
Carlos and Th completed the same amount of passes
hope this helps
Carlos was 7 out of 10 = 7/10= 0.7 = 70%
Th was 21 out of 30 = 21/30 = 0.7 = 70%
they have the same rate
Sheila is going to divide a 36 inch piece of ribbon into 5 equal pieces she says each piece will be 7 inches long what is Sheila’s error
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a band made 8,000 copies of an album they sold 6,280 copies how many copies are left
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Hope this helps!
Can u plz mark me as brainliest? I really need it!
What is the value of x? Enter your answer in the box. x =
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................
Help me please To solve the task Mrs. Hilt had $4,000 in her savings account. She earned 10% interest each year. If she left that money in the account for one year, how much will she have in the account at the end of that year?
Answers
Mrs. Hilt will have $4,400 in her savings account at the end of one year after earning 10% interest on her initial $4,000 deposit.
To solve the task of determining how much Mrs. Hilt will have in her savings account after one year, we need to calculate the interest earned and add it to the original amount. Mrs. Hilt has $4,000 in her account, and the annual interest rate is 10%.
The interest Mrs. Hilt will earn in one year is calculated by multiplying the principal amount by the interest rate: $4,000 x 0.10 = $400. Therefore, the total amount in the account after one year, which includes the original principal and the interest earned, is $4,000 + $400 = $4,400.
In summary, Mrs. Hilt will have $4,400 in her savings account at the end of one year, based on a 10% annual interest rate.
Tom Quig traveled 260 miles east of St. Louis. For most of the trip he averaged 60 mph, but for
3)
one period of time he was slowed to 20 mph due to a major accident. If the total time of travel was
7 hours, how many miles did he drive at the reduced speed?
Answers
260 minus 180 is 80. 80 divided by 20 is 4.
4 plus 3 is 7
Write the equation in slope-intercept form:
x - y = 4
Question 8 options:
a) y = -4x
b) y = x - 4
c) y = 4x
d) y = x/4
Answers
On a map of Illinois, the distance between Chicago and Algonquin is 3.2 centimeters. If 2 centimeters = 40 kilometers, what is the approximate distance between the two cities?
Answers
Final answer:
The approximate distance between Chicago and Algonquin is 64 kilometers.
Explanation:
To find the approximate distance between Chicago and Algonquin, we can use the given scale of 2 centimeters = 40 kilometers. Since the distance on the map is 3.2 centimeters, we can set up a proportion to find the actual distance:
2 cm / 40 km = 3.2 cm / x km
Cross multiplying, we get 2x = 40 x 3.2, which simplifies to 2x = 128. Dividing by 2, we find that x is equal to 64. Therefore, the approximate distance between Chicago and Algonquin is 64 kilometers.
the cost of the fabric is $1.31. what would you expect to pay for a similar piece of fabric that is 18 inches by 42 inches?
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Calculate areas for 2 rectangles;
21*9= 189
18*42= 756
make an equation with data you have;
If 189 cost $1.31
756 cost $x
_____________
756 *1.31 / 189 = $5.24 cost for second fabric
Second way;
(18x42) / (21x9) = 4 x 1.31 = $5.24
Which ever you find easer
Approximately $991.56 for a similar piece of fabric that is 18 inches by 42 inches, assuming the cost per square inch remains the same.
To calculate the cost of a similar piece of fabric that is 18 inches by 42 inches, you need to first determine the area of the fabric in square inches and then multiply it by the cost per square inch.
The area of the fabric is given by the formula:
Area = Length × Width
In this case, the length is 18 inches, and the width is 42 inches. So,
Area = 18 inches × 42 inches = 756 square inches
Now that you have the area of the fabric, you can calculate the cost. If the cost of the fabric is $1.31 for 1 square inch, then you can simply multiply the cost per square inch by the total area:
Cost = Cost per square inch × Area
Cost = $1.31 × 756 square inches
Now, calculate the cost:
Cost = $991.56
So, you would expect to pay approximately $991.56 for a similar piece of fabric that is 18 inches by 42 inches, assuming the cost per square inch remains the same.
for such more question on area
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what fraction is a equivalent to 0.1. repeating
Answers
10x=1.1...
x=0.1...
Then subtract the two equations from each other:
9x=1
Solve for x:
x=1/9
Consider the equation .(-22+3x/3x+7)=2
How do you begin isolating the variable x to one side of the equation? Multiply both sides by 3x + 7. Divide both sides by 3x + 7. Multiply both sides by -22 + 3x. Divide both sides by -22 + 3x. _______
The solution of the equation is______
Answers
Answer: The solution of the above equation would be -12.
and First option is correct " Multiply both sides by 3x + 7."
Step-by-step explanation:
Since we have given that
[tex]\dfrac{-22+3x}{3x+7}=2[/tex]
First we multiply (3x+7) on both sides , we get
[tex]-22+3x=2(3x+7)[/tex]
And then we will solve it for the value of 'x'.
[tex]-22+3x=6x+14\\\\-22-14=6x-3x\\\\-36=3x\\\\\dfrac{-36}{3}=x\\\\-12=x[/tex]
Hence, the solution of the above equation would be -12.
and First option is correct " Multiply both sides by 3x + 7."
Answer:
Multiply both sides by 3x + 7. Divide both sides by 3x + 7. Multiply both sides by -22 + 3x. Divide both sides by -22 + 3x
Step-by-step explanation:
Deon plans to ride a 15 mile bicycle trail. If his average speed 20 mile per hour which equation can he use to find the time t in hour for the ride
Answers
Answer:
See below
Step-by-step explanation:
Distance = rate * time
Distance / rate = time
15 / 20 = time = 3/4 hr = 45 min
Harriet counts 15 big boxes and 12 small boxes of notebooks. Each large box contains 189 notebooks, and each small box contains 79 notebooks. Estimate the total number of notebooks. Is your estimate an overestimate or an underestimate? Explain why it is better to have an overestimate than an underestimate.
Answers
Like terms that have the same ____,with each variable raised to the same exponent.
A. Operation(s)
B. Variable(s)
C. Expression(s)
D. Exponent(s)
Answers
12 tickets for $4.68 or 10 tickets for $4.50
Answers
4.50/10 = 0.45 per ticket.
So, we are better off taking 12 tickets for $4.68
Hope this helps!
Betsy participates in a scavenger hunt that requires her to retrieve items from 4 locations. The locations are on a map with the coordinates as given:
Location 1 is at (−4, −1) .
Location 2 is at (−4, 4) .
Location 3 is at (3, 4) .
Location 4 is at (3, −1) .
The paths from one location to another are straight lines. One unit on the coordinate grid equals 10 yd. Betsy starts at location 1 and goes to location 2, then location 3, and then location 4, and then returns back to location 1.
What is the total distance Betsy has traveled?
Answers
Answer:
240 yd
Step-by-step explanation:
Let A, B, C, and D represent location 1, location 2, location 3, and location 4 respectively.
Consider the figure in the attached file.
We need to find the total distance traveled by Betsy.
The distance covered by Betsy is
length of segment AB[tex]+[/tex] length of segment BC[tex]+[/tex] length of segment CD[tex]+[/tex] length of segment DA.
To find the distance AB, we need to find the distance from A to B on y-axis.
So, length of segment AB [tex]=5 [/tex] units
To find the distance BC, we need to find the distance from B to C on x-axis.
So, length of segment BC [tex]=7 [/tex] units
To find the distance CD, we need to find the distance from C to D on y-axis.
So, length of segment CD [tex]=5 [/tex] units
To find the distance DA, we need to find the distance from D to A on x-axis.
So, length of segment DA [tex]=7 [/tex] units
Hence, the total distance covered is [tex]5+7+5+7=24[/tex] units
It is given that 1 unit equals 10 yd, so distance traveled by Besty is [tex]10\times 24=240[/tex] yd
How do I solve this math Distribute and Combine Like Terms Maze -4(3-5x)-4x
Answers
-12+20x-4x
Combine like terms:
-12+16x
and you are done
A book has a front and a back and 400 pages. The front and back cover are each 0.9mm thick measured to 1 decimal place. Each page is 0.13 mm thick measured to 2 decimal places. Calculate the minimum thickness of the book.
Answers
Answer:
Step-by-step explanation:
0.9 UB=0.95
0.9 LB=0.85
0.13 UB= 0.135
0.13 LB= 0.125
0.85x2=1.7
0.125x400=50
1.7+50=51.7
Minimum thickness=51.7mm
To calculate the minimum thickness of the book, add up the thickness of the front cover, the back cover, and all the pages. The minimum thickness of the book is 54.8mm.
Explanation:To calculate the minimum thickness of the book, we need to add up the thickness of the front cover, the back cover, and all the pages. The front cover has a thickness of 0.9mm, the back cover has a thickness of 0.9mm, and each page has a thickness of 0.13mm. There are 400 pages in the book. So, the minimum thickness of the book can be calculated as:
Front cover thickness + Back cover thickness + (Number of pages x Page thickness)
0.9mm + 0.9mm + (400 x 0.13mm) = 0.9mm + 0.9mm + 52.0mm = 54.8mm
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15=7-x find x please
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Given: ΔXYZ
XY = 28 cm; XZ = 30 cm; YZ = 32
AB is a midsegment parallel to XY
What is the length of AB?
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Answer:
I think the answer is
7cm
Answer:
The correct answer should be 7cm if not 14cm
3y+11 plus 7x-30 plus 5x+14 find x and the y
Answers
3y + 12x - 5
3y = -12x + 5
y = (-12x + 5)/3
x = (3y - 5)/-12
hope this helps
tasha fnished a job in 3/4 hour. megan finished it in 4/5 of the time tasha took. how long did megan take to finish the job?
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4/5 of 45 min = 36 min
Megan took 36 min to finish the job
Drag and drop numbers into the boxes so that the paired values are in a proportional relationship.
Answers
The answer is 6
Karita had $138.72 in her checking account. She wrote checks for $45.23 and $18.00. Then she made a deposit of $75.85 into her account