AP Calculus
Worksheet
Section 1.3
Name ________________________________________hr 4
1. Graph the function. State its domain and range.
2. Rewrite the exponential expression to have the
indicated base.
y  3  ex  2
16 3 x , base 2
Date ____/____/____ Score:________/
= ________%
Domain:____________________________________
Range: ____________________________________
___________________________
Use a graph to find the zeros of the function. Sketch the graph and circle the zeros.
3. f ( x)  2 x  5
4. f ( x)  3  2 x
zeros: ____________________________________
zeros: ____________________________________
Match the function with its graph. Try to do it without using your grapher.
5. y  3 x __________
6.
y  1.5 x  2 __________
Use an exponential mode to solve the problem.
7. Radioactive Decay
The half-life of phosphorous-32 is about 14 days. There
are 6.6 grams present initially.
(a) Express the amount of phorphous-32 remaining as a
function of time.
(b) When will there be 1 gram remaining?
8. Finding Time
If John invests $2300 in a savings account with a 6%
interest rate compounded annually, how long will it
take until John’s account has a balance of $4150.
(a)_______________
(b) ______________
______________
9. Doubling Your Money
Determine how much time is requires for an investment
to double in value if interest is earned at the rate of 6.25%
compounded annually.
10. Doubling Your Money
Determine how much time is requires for an investment
to double in value if interest is earned at the rate of
6.25%compounded monthly.
______________
______________
11. Doubling Your Money
Determine how much time is required for an investment
to double in value if interest is earned at the rate of
6.25% compounded continuously.
12. Eliminating Disease
Suppose that any given year, the number of cases of a
disease is reduced by 20%. If there are 10,000 cases today,
how many years will it take
(a) to reduce the number of cases to 1,000?
(b) to eliminate the disease; that is , to reduce the number of
cases to less than 1?
(a)_______________
______________
(b) ______________
Copy and complete the table for the function.
13. y  2 x  3
x
1
2
3
4
y
y
?
?
?
?
14. y  3e x
x
1
2
3
4
?
?
?
y
?
?
?
?
Ratio: yi ( y )
i 1
?
?
?
15. Population of California
Table 1.12 gives the population of California for several years.
Table 1.12
1980
Population of
California
(thousands)
23,688
1990
29,811
1995
31,697
1998
32,988
1999
33,499
2000
33,872
(a) Let x =0 represent 1980, x = 1 represent 1981, and so forth.
Find an exponential regression for the data, and superimpose
its graph on a scatter plot of the data.
(b) Use the exponential regression equation to estimate the
population of California in 2003. How close is the estimate
to the actual population of 35, 484,000 in 2003?
(c) Use the exponential regression equation to estimate the
annual rate of growth of the population of California.