Download Name______________________________ Algebra II 7.2

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Algebra II
7.2 - 7.3 Worksheet
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Date ______________________Hour ____
In #1 – 6, tell whether the function represents exponential growth or exponential decay.
74 x
87 x
1. f ( x)  2
2. f ( x)  3
3. f ( x)  130.34 
x
4. f ( x )  53  4 x
5. f ( x )  13  e x
6. f ( x ) 8e  x
In # 7 – 11, graph each function without a calculator. Include 5 ordered pairs in each table. Give the domain and range.
Give the equation for the horizontal asymptote.
7. f ( x) 
15 x
x
y
Domain:
Range:
Asymptote:
8. f ( x) 
14 x
x
y
Domain:
Range:
Asymptote:
15 x
9. f ( x)  2
x
y
Domain:
Range:
Asymptote:
10. f ( x) 
13 x  1
x
y
Domain:
Range:
Asymptote:
11.
f ( x)  2 14   1
x
x
y
Domain:
Range:
Asymptote:
12. What is an asymptote of the graph of y 
A)
y  3
13 x3  5 ?
B) y  3
13. What is an asymptote of the graph of y   12 
x 2
A)
y  3
B) y  2
C) y  5
D) y  5
C) y  2
D) y  3
 3?
14. You invest $500 in the stock of a company. The value of the stock decreases 2% each year. Describe and correct the error
in writing the a model for the value of the stock after t years.
y  initial amount Decay factor 
t
y  500 0.02
t
15. You invest $600 in the stock of a company. The value of the stock decreases 3.5% each year.
a) Write a model for the value of the stock after x years.
b)
Find the value of the stock after 7 years.
16. You buy a new car for $28,999. The value of the car decreases by 16% each year.
a) Write an exponential decay model giving the car’s value (in dollars) after x years.
b) What is the value of the car after 5 years?
17. You buy a new mountain bike for $200. The value of the bike decreases by 25% each year.
a) Write a model giving the bikes value y (in dollars) after t years.
b) What is the value of the bike after 3 years?
18. When a plant or animal dies, it stops acquiring carbon-14 from the atmosphere. Carbon-14 decays over time with a
half life of about 5730 years. The percent P of the original amount of carbon-14 that remains in a sample after t years
is given by the equation below. What percent of the original carbon-14 remains in a sample after 2500 years?
19. The number of E of eggs a leghorn chicken produces per year can be modeled by the equation E  179.20.89
w
52
where w is the age (in weeks) of the chicken and w  22. Estimate the egg production of a chicken that is 2.5 years
old.
In # 20 – 27, simplify each (no calculator).


3
20.
e5  e 4
21.
e 7  e 2
22.
3e 2  5e 3
23. 2e 5 x
24.
2e 
25.
5e 
26.
e x  e 5 x  e 3
27. e x  8e x 5
6 4
27e 9 x
?
3e 5 x 7
28. What is the simplified form of
A)
9
2
e4 x8
6 x 1
2 4
B) 3e x
4 8
C) 3e x
D)
9
2
e2 x 4
In # 29 – 32, use a calculator (nearest hundredth) to evaluate each expression.
29.
e5
30.
e
7
2
31. 12e
5
3
2.4
32.  9e
33. The number of camera phones shipped globally can be modeled by the function y  1.37e
where x is the
number of years since 1998 and y is the number of camera phones shipped (in millions). How many camera phones
were shipped in 2006?
1.43 x
34. Scientists used traps to study subterranean termite populations in New Orleans. The mean number of y termites
collected annually can be modeled by y  728e
number of termites collected in 2000?
0.329t
where t is the number of years since 1986. What is the mean
35. You deposit $3500 in an account that pays 3% annual interest compounded continuously. What is the balance
after 5 years?
36. In 2009, you deposit $12,000 in an account that pays 2.35% annual interest compounded continuously. What is
the balance in 2013?