Answer:
[tex]\boxed{\boxed{a = 240, b = 1.16}}[/tex]
Step-by-step explanation:
General exponential function for growth or decay is,
[tex]y=a(1\pm r)^{x}[/tex]
Where,
a = initial value,
r = rate of change
+ is used for growth and - is used for decay.
As here, the number of birds increasing so, the exponential function is,
[tex]y=a(1+r)^{x}[/tex]
And initial value a = 240, r = rate of change = 16% = 0.16
Putting the values,
[tex]y=240(1+0.16)^{x}\\\\y=240(1.16)^{x}[/tex]
Comparing this with the given equation [tex]y=ab^{x}[/tex]
Hence, a = 240, b = 1.16
Answer:
The value of a is 240 and b is 1.16.
Step-by-step explanation:
Given,
The initial population of the birds = 240,
Annual rate of increasing = 16 %,
Hence, the population of birds after x years
[tex]P=240(1+\frac{16}{100})^x[/tex]
[tex]=240(1+0.16)^x[/tex]
[tex]=240(1.16)^x[/tex]
We can put P = f(x), ( because, f(x) also shows the population of birds after x years )
[tex]\implies f(x) = 240(1.16)^x[/tex] --------(1)
According to the question,
[tex]f(x) =ab^x[/tex] --------(2),
From equation (1) and (2),
a = 240 and b = 1.16
Which of the following is a factor of 2x4 + 22x3 + 60x2?
2x3
x4
x + 4
x + 5
Answer
One factor of the equation [tex]2x^{4} + 22x^{3} + 60x^{2}[/tex] is x + 5 .
Option (d) is correct.
Reason
As the equation in the question is as follows
[tex]= 2x^{4} + 22x^{3} + 60x^{2}[/tex]
simplify the above
Taking 2x² as a common part
= 2x²(x² + 11x + 30 )
= 2x² (x² + 5x + 6x + 30)
= 2x²(x(x+5) +6(x + 5))
= 2x²(x + 5)(x + 6)
Therefore the factors are 2x² , (x +5) , (x + 6) .
52.063 divided into 9.2 rounded to the nearest hundredth
Answer:
The answer is 5.66
Step-by-step explanation:
52.063 divided by 9.2 is 5.65902173913. Then you round of to the nearest hundredth which is two decimal places to the right (so it's 5). Then you round it off one value higher since 9 is above 5. Therefore the final answer is 5.66
Mark has a baking tray with 24 muffins and the muffin are arranged in 4 equal rows how many are there in each row
What is 35/10 convert into a decimal?
What is the area of ABC below? If necessary, round your answer to two decimal places.
The answer I got from apex was- 106.26
A model rocket is launched with an initial upward velocity of201ft/s . The rocket's height h (in feet) after t seconds is given by the following. h=201t -16t^2
Find all values of for which the rocket's height is 93 feet.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
...?
The values for which the rocket's height is 93 feet are t = 0.48 seconds and 12.08 seconds.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
We have:
A model rocket is launched with an initial upward velocity of 201ft/s.
The rocket's height h (in feet) after t seconds is given by the following:
h = 201t -16t²
The above equation is parabolic.
Plug h = 93 feet
93 = 201t - 16t²
16t² - 201t + 93 = 0
After solving with the quadratic formula:
[tex]\rm t_{1,\:2}=\dfrac{201\pm \sqrt{201^2-4\left(16\right)\left(93\right)}}{2\left(16\right)}[/tex]
t = 0.481, 12.081
or
t = 0.48, 12.08 secods
Thus, the values for which the rocket's height is 93 feet are t = 0.48 seconds and 12.08 seconds.
Learn more about the parabola here:
brainly.com/question/8708520
#SPJ2
You drive your car for 3 hours at an average speed at 30 km per hour. how far did you go?
4x-6=10x-3
?? i am bad at math lol
Heather has $500 in her savings account. she withdraws $20 per week for gas. write an equation heather can use to see how many weeks it will take her to have a balance of $220.
please help me I really need it.
Answer:
(x, y, z) = (-5, -1, 0) (x, y, z) = (-8, -7, 5)Step-by-step explanation:
1. A graphing calculator or equation-solving web site can tell you the solution is (-5, -1, 0).
As is sometimes the case with multiple-choice questions, you can choose the "consensus answer".
For x, -5 appears in 3 of 4 answer choices.
For y, -1 appears in 3 of 4 answer choices.
For z, 0 appears in 3 of 4 answer choices.
Thus, the "consensus" is that the answer is (-5, -1, 0). Choosing this one to check can shorten the work of checking the answer choices.
-5 +5(-1) +4(0) = -10 . . . first equation can use this answer2(-5) -(-1) +5(0) = -9 . . . second equation can use this answer2(-5) -10(-1) -5(0) = 0 . . . third equation can use this answerSo, by "guess and check" we have determined the solution to be (-5, -1, 0).
__
2. First of all, you can substitute the given value of z into the other two equations. Then you have ...
2x -y +5 = -4-2x +3y -5 = -10The first of these equations can be solved for y:
y = 2x +9
and this can be substituted for y in the second of these equations:
-2x +3(2x +9) -5 = -10
4x +22 = -10
4x = -32
x = -8
and ...
y = 2(-8) +9 = -7
So this solution, too, is the "consensus solution," ...
(x, y, z) = (-8, -7, 5)
Use the function described below to answer questions 1 - 4.
Yvonne invested $4,000 in a savings account which pays 3.5% interest compounded annually. Use the formula A = P(1 + r)t, where P is the principal, r is the interest rate, and t is the time in years.
1. Approximately, how much money will Yvonne have in 4 years? Round to the nearest cent.
2. Approximately, how much money will Yvonne have in 8 years? Round to the nearest cent.
3. Approximately, how many years will it take for Yvonne to double her money? Write the number of years only.
4 Alex buys a top of the line computer. He did not realize that the computer would lose value so fast. If his computer cost $1800.00 and it depreciates at a rate of 45% each year, in how many years will it be worth less than 1/3 of what he paid for it?
0.00014s in scientific notation? ...?
Explain how you use the bar model to solve 14-7 equal seven
Describe the kernel and range of (a) the orthogonal projection on the xz -plane (b) the orthogonal projection on the yz-plane (c) the orthogonal projection on the plane defined by the equation y=x ...?
Lauren bought 6 yellow roses, 10 orange roses, and 12 pink roses to make a bouquet. What is the ratio of the number of yellow roses to the total number of roses in Lauren’s bouquet?
The price of a pair of shoes is $63.20. The sales tax rate is 4.5 percent. How much sales tax would you pay if you bought these shoes? A.) $2.84 B.) $3.16 C.) $4.50
a cable installer charges $42.50 per hour plus a $45.00 service charge. your fathers firm hires him to hook up his companys internet service. find the total charges if it takes the cable installer 5 hours to complete the task? ...?
Answer: $257.50
Step-by-step explanation:
Total charges of 5 hours paid by father = Charges of cable installer for 5 hours + Service Charge
Charges of cable installer per hour = $42.50
Charges of cable installer for 5 hours = 5 × 42.50 = $212.50
Additional service charge by him = $45.00
So, total charges of 5 hours paid by father = $212.50 + $45.00 = $257.50
A 13 foot ladder is leaning against a wall. If the point where the ladder meets the wall is 12 feet above the ground, how far from the base of the wall is the the ladder?
A) 1 foot
B) 2 feet
C) 5 feet
D) 22 feet
if (3x^2)+7=0 then (x-1/3)^2
In the fall, you go to the local nursery and purchase a package of 10 rose plants. The clerk informs you that on average you can expect 5% of the plants to not live through the winter. Assume that the plants are a random sample.
a) Use the binomial formula to determine the probability that one or more of the plants will not survive the winter.
b) What is the probability that all the plants will survive? Write how the binomial formula is used to calculate the probability.
whats x?
16x - 4x = -48
If possible, can you show your steps
Denver is called the mile-high city because it is at an altitude of 1 mile. how many feet is the
Write the distribution of 7×6=
two consecutive odd negative integers have a product of 483, find the integers ...?
Bill makes four payments a year of $128.25 for life insurance; four payments of $161.82 for real estate taxes; twenty-four payments of $37.46 for health insurance; and six payments of $221.65 for auto insurance. What is the total of his annual fixed expenses for these items?
To calculate the total annual fixed expenses, we multiply the number of yearly payments by the amount of each payment for the different insurances and taxes, and then add these products together to find that the annual fixed expenses total $3,388.74.
The student has asked to calculate the total of his annual fixed expenses for life insurance, real estate taxes, health insurance, and auto insurance. To determine this, we will multiply the amount of each payment by the number of times the payment is made annually and then sum these amounts to get the total yearly expense:
Life Insurance: 4 payments of $128.25
Real Estate Taxes: 4 payments of $161.82
Health Insurance: 24 payments of $37.46
Auto Insurance: 6 payments of $221.65
Now, we calculate each:
Life Insurance: 4 imes $128.25 = $513.00
Real Estate Taxes: 4 imes $161.82 = $647.28
Health Insurance: 24 imes $37.46 = $898.56
Auto Insurance: 6 imes $221.65 = $1,329.90
Adding these amounts gives us the total annual fixed expenses:
$513.00 (Life Insurance) + $647.28 (Real Estate Taxes) + $898.56 (Health Insurance) + $1,329.90 (Auto Insurance) = $3,388.74 as the annual fixed expenses.
$29,000;$4 decrease find the new amount given the original amount and the percent of change.
A student gets paid to sell raffle tickets at the school basketball game. He earns $15 a day, plus an extra $0.25 for each raffle ticket he sells and $2 for each hour he works at the game. If d = days, r = raffle tickets, and h = hours, what function can he use to calculate his earnings?
Answer: C. [tex]T=15d+\frac{r}{4}+2h[/tex]
Step-by-step explanation:
Let d = days, r = raffle tickets, and h = hours.
Given: A student earns in a day = $15
Then his earning in d days =$15d
Also, he earns for each riffle = $0.25
Then his earning in for r riffles =$0.25r
And , he earns for each hour he works at the game = $2
Then his earning for h hours = $2h
Then the function he can use to calculate his earnings is given by :_
[tex]T=15d+0.25r+2h\\\\\Rightarrow\ T=15d+\frac{1}{4}r+2h[/tex]
How does the graph of g(x) 1/x+4-6 compare to the graph of the parent function f(x) 1/x
g(x) is shifted 4 units right and 6 units up from f(x).
g(x) is shifted 4 units right and 6 units down from f(x).
g(x) is shifted 4 units left and 6 units up from f(x).
g(x) is shifted 4 units left and 6 units down from f(x).
Answer:
Option 4- Graph of g(x) is shifted 4 units left and 6 units down from f(x).
Step-by-step explanation:
Given : Graph of [tex]g(x)=\frac{1}{x+4}-6[/tex]
To find : How does the graph of g(x) compare to the graph of the parent function [tex]f(x)=\frac{1}{x}[/tex]
Solution :
The graph f(x) is being translated to form the graph g(x).
In graph [tex]g(x)=\frac{1}{x+4}-6[/tex] there is
Translation of 4 unit left and 6 unit downward.
In graph f(x) if we shift the graph with 4 unit left it form
f(x)→f(x+b) , the function is shifted towards left with b unit.
So, [tex]f(x)=\frac{1}{x+4}[/tex]
In graph f(x) if we shift the graph with 6 unit downward it form
f(x)→f(x)-a , the function is shifted downward with a unit.
So, [tex]f(x)=\frac{1}{x+4}-6[/tex]
Therefore, Option 4 is correct.
Graph of g(x) is shifted 4 units left and 6 units down from f(x).
How to do 4 3/4 -9 2/3?
what is the value?
5x+3=4x ?? bit confused