Download Quiz Review – Exponential Functions Name: AFM Directions

Quiz Review – Exponential Functions
AFM
Name: ______________________________
Directions: Evaluate each of the following using: 𝑓(𝑥) = 1.3(0.8)𝑥
1. 𝑓(−2.9) =
2. 𝑓(0) =
3. 𝑓(6) =
4. 𝑓(𝜋) =
5. Graph g(x) using a table (choose your own x-values).
x
g(x)
𝑔(𝑥) = 5(0.2)𝑥
6. Graph ℎ(𝑥) = 5(2.2)𝑥 on your calculator and compare to the graph of g(x) from #5. Explain how the
base of an exponential function determines the shape of the graph (1-2 sentences).
7. Graph 𝑗(𝑥) = 0.5(0.2)𝑥 on your calculator and compare to the graph of g(x) from #5. Explain how
the coefficient of an exponential function determines the shape of the graph (1-2 sentences).
8. Graph 𝑘(𝑥) = −5(0.2)𝑥 on your calculator and compare to the graph of g(x) from #5. Explain how
switching a coefficient from a positive to a negative affects the shape of an exponential graph (1-2
sentences).
Directions: Use this data for #9-12.
Some biologists are growing bacteria in a laboratory. They count the number of bacteria every two days:
Time in days 0
Cell Count
597
2
893
4
1339
6
1995
8
2976
10
4433
12
6612
14
9865
9. Find the exponential regression equation of the data 11. Explain what the y-intercept means in the context
(round to at least 3 decimal places).
of this data (1-2 sentences).
10. Identify the y-intercept of the regression equation. 12. Use the equation to predict the number of bacteria
cells after 20 days.
Directions: Use this scenario for #13-15.
A person puts money into a savings account where the interest is compounded continuously at an annual rate of
1%. The amount of money in the account can be modeled by: 𝐴(𝑥) = 3000𝑒 0.01𝑥 where A(x) is the amount of
money after x years.
13. How much money is in the
account after 10 years?
14. Determine the amount of
money that was initially deposited
when the account was opened.
15. How would the equation
change if the interest rate was 4%
instead of 1% ?
Directions: Use this scenario for #16-18.
Radioactive gallium-67 decays by 1.48% every hour; there are 100 milligrams initially.
16. What percentage of gallium-67
remains in the sample after each
hour?
17. Write a function to model the
18. Use the function to predict the
amount (in milligrams) of gallium- amount of gallium-67 in the sample
67 that remains in the sample after t after 24 hours.
number of hours.
(Answer Key)
Directions: Evaluate each of the following using: 𝑓(𝑥) = 1.3(0.8)𝑥
1. 𝑓(−2.9) =
2. 𝑓(0) =
3. 𝑓(6) =
4. 𝑓(𝜋) =
2.483
1.3
0.341
= 1.3(0.8)𝜋 = 0.645
5. Graph g(x) using a table (choose your own x-values).
𝑔(𝑥) = 5(0.2)𝑥
x
g(x)
-1
25
0
5
1
1
2
0.2
3
0.04
6. Graph ℎ(𝑥) = 5(2.2)𝑥 on your calculator and compare to the graph of g(x) from #5. Explain how the
base of an exponential function determines the shape of the graph (2-3 sentences).
A: The graph would be an exponential growth model instead of exponential decay. If the base is between 0 and
1, the graph is decreasing, but if the base is greater than 1, the graph increases.
7. Graph 𝑗(𝑥) = 0.5(0.2)𝑥 on your calculator and compare to the graph of g(x) from #5. Explain how
the coefficient of an exponential function determines the shape of the graph (1-3 sentences).
A: The graph would still have the same direction, but it would decrease more slowly as x gets larger. Larger
coefficients make graphs increase or decrease more sharply, while smaller coefficients (between 0 and 1) make
the graph increase or decrease more gradually and slowly.
8. Graph 𝑘(𝑥) = −5(0.2)𝑥 on your calculator and compare to the graph of g(x) from #5. Explain how
switching a coefficient from a positive to a negative affects the shape of an exponential graph (1-2
sentences).
A: Switching the coefficient from a positive to a negative will flip the graph over the x-axis. This means that all
function values will be negative instead of positive. The graph will never go above 0 instead of never going
below 0.
Directions: Use this data for #9-12.
Some biologists are growing bacteria in a laboratory. They count the number of bacteria every two days:
Time in days 0
Cell Count
597
2
893
4
1339
6
1995
8
2976
10
4433
12
6612
14
9865
9. Find the exponential regression equation of the data 11. Explain what the y-intercept means in the context
(round to at least 3 decimal places).
of this data (1-2 sentences).
Use calculator: 𝑦 = 598.941(1.222)𝑥
It means that at the beginning of the first day (time
=0), there were 598.941 bacteria cells.
10. Identify the y-intercept of the regression equation. 12. Use the equation to predict the number of bacteria
cells after 20 days.
Plug in 0 for x: 𝑦 = 598.941(1.222)0 = 598.941
Plug in 20 for x: 𝑦 = 598.941(1.222)20 =
so y-intercept is (0, 598.941)
33022.364 so there would be 33,022 bacteria after
20 days.
Directions: Use this scenario for #13-15.
A person puts money into a savings account where the interest is compounded continuously at an annual rate of
1%. The amount of money in the account can be modeled by: 𝐴(𝑥) = 3000𝑒 0.01𝑥 where A(x) is the amount of
money after x years.
13. How much money is in the
account after 10 years?
14. Determine the amount of
money that was initially deposited
when the account was opened.
Plug in 10 for x:
3000𝑒 0.01(10) = 3315.51 so
Plug in 0 for x: 3000𝑒 0.01(0) =
$3,315.51 *Remember to put the
3000 so $3,000 *Remember to
entire exponent in parentheses when put the entire exponent in
using calculator*
parentheses when using calculator,
if not you will just get 0*
15. How would the equation
change if the interest rate was 4%
instead of 1% ?
𝑦 = 3000𝑒 0.04𝑥
Directions: Use this scenario for #16-18.
Radioactive gallium-67 decays by 1.48% every hour; there are 100 milligrams initially.
16. What percentage of gallium-67
remains in the sample after each
hour?
98.52% remains (because 1.48%
has decayed, so take 100% –
1.48%)
17. Write a function to model the
18. Use the function to predict the
amount (in milligrams) of gallium- amount of gallium-67 in the sample
67 that remains in the sample after t after 24 hours.
number of hours.
100(. 9852)24 = 69.917 mg
𝑓(𝑡) = 100(. 9852)𝑡
remaining