Download Name Date Test Review Exponentials Standard: MCC9

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Date ________________________
Test Review Exponentials
Standard: MCC9-12.A.CED.2 Create equations in two or more variables to represent relationships between
quantities; graph equations on coordinate axes with labels and scales.
3 𝑡
1. After t years, the value of a car that costs $20,000 is modeled by 𝑦 = 20000 (4) . Determine the value of
the car 2 years after it was purchased.
2. If the annual rate of inflation averages 4% over the next 10 years, the approximate cost of goods and
services during any year in that decade will be modeled by 𝑦 = 𝑃(1.04)𝑡 where t is the time in years and P is
the present cost. If the price of an oil change for your car is presently $23.95, estimate the price 10 years
from now.
3. The population of Augusta increases according to the model 𝑦 = 195,844(1.003)𝑡 since 2010. If t
represents the time since 2010, what will the population of Augusta be in the year 2013?
4. Does the following set of ordered pairs represent an exponential equation? If so, state the initial (starting)
amount, the common ratio (multiplier) and general form of the equation (Eq).
a.
b.
c.
d.
x
y
x
y
x
y
x
y
-1
4
0
1
1
6
-2
24
0
8
1
½
2
18
-1
12
1
16
2
¼
3
54
0
6
2
32
3 1/16
4 162
1
3
3
64
4 1/32
5 486
2
3/2
Initial:
Ratio:
Eq:
Initial:
Ratio:
Eq:
Initial:
Ratio:
Eq:
Initial:
Ratio:
Eq:
5. What is the rate of growth or decay?
a. 𝑦 = 1.13
Graph the following:
6. 𝑦 = 1.5(2)𝑥
b. 𝑦 = 7(0.45)𝑡
7. 𝑦 = 4(3)𝑥
1 𝑟
c. 𝑦 = 1.7 (4)
d. 𝑦 = 1.2(1.63)2
8. 𝑦 = 3(0.5)𝑥
Simple Interest
y  a(1  r ) x
Decay
y  a(1  r ) x
Compound Interest
r
A  p (1  ) nt
n
Growth/Decay
y  a  bx
9. Ants are invading your kitchen; you notice that the ants seem to triple over night. After initially noticing
three ants, how many ants do you suspect will be in your kitchen after 7 nights?
10. A negative affect on a local eco-system is largely due to a herd of bison in Wyoming. There is a concern
that within 10 years the herd will top 5,000. The herd has a growth rate that doubles every 5 years. With a
current herd size of 1500, is the concern valid? Why or why not?
11. Scientist have determined that the bison herd in Wyoming has a 10% annual growth rate. Given the
initial herd of 1500, what will be the size of the herd after 8 years?
12. The Class of 2016 decided to collect money this year for their 25th Class Reunion! They were able to
collect $13,145.17. A local bank has offered to place the money into an account that earns 6% interest on
average. Given that their 25th Class Reunion will happen 29 years from now, how much money will be in the
account?
13. You are looking to invest $15,000. You have visited two banks. Bank A offers a 1.33% rate compounding
quarterly for 10 years. Bank B offers a 1.30% rate compounding weekly for 10 years. Which bank offer will
you select and why?
14. Purchasing a Car: You plan to keep a recently purchased car for 3 years. If you purchase the car for
17,541.00 and it is expected that the value will decrease at a rate of 15% annually, what will be the car’s value
at the end of 3 years?
If your payments are $280.00 per month, do you think you made a good investment? Explain (there
are no right or wrong answers for this part of the question).