Algebra II Unit 8 Reveiw
Unit 8 Exponential Functions Review Packet
Short Answer
Graph the exponential function.
1.
2.
3. An initial population of 505 quail increases at an annual rate of 23%. Write an exponential function to model the quail population.
4. Write an exponential function for a graph that includes (1, 15) and (0, 6).
5. For an annual rate of change of –31%, find the corresponding growth or decay factor.
6. Graph .
7. The half-life of a certain radioactive material is 85 days. An initial amount of the material has a mass of 801 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 10 days. Round your answer to the nearest thousandth.
8. Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will you have in the account after 4 years?
Write the equation in logarithmic form.
9.
10.
Evaluate the logarithm.
11.
12.
13. Write the equation in exponential form.
Graph the logarithmic equation.
14.
Write the expression as a single logarithm.
15.
16.
17.
Expand the logarithmic expression.
18.
19.
20.
21. Solve . Round to the nearest ten-thousandth.
22. Use the Change of Base Formula to evaluate . Then convert to a logarithm in base 3. Round to the nearest thousandth.
23. Solve .
24. Solve .
Write the expression as a single natural logarithm.
25.
26. The sales of lawn mowers t years after a particular model is introduced is given by the function y = , where y is the number of mowers sold. How many mowers will be sold 2 years after a model is introduced? Round the answer to the nearest whole number.
27. The generation time G for a particular bacteria is the time it takes for the population to double. The bacteria increase in population is shown by the formula , where t is the time period of the population increase, a is the number
Short Answer
Graph the exponential function.
1.
2.
3. An initial population of 505 quail increases at an annual rate of 23%. Write an exponential function to model the quail population.
4. Write an exponential function for a graph that includes (1, 15) and (0, 6).
5. For an annual rate of change of –31%, find the corresponding growth or decay factor.
6. Graph .
7. The half-life of a certain radioactive material is 85 days. An initial amount of the material has a mass of 801 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 10 days. Round your answer to the nearest thousandth.
8. Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will you have in the account after 4 years?
Write the equation in logarithmic form.
9.
10.
Evaluate the logarithm.
11.
12.
13. Write the equation in exponential form.
Graph the logarithmic equation.
14.
Write the expression as a single logarithm.
15.
16.
17.
Expand the logarithmic expression.
18.
19.
20.
21. Solve . Round to the nearest ten-thousandth.
22. Use the Change of Base Formula to evaluate . Then convert to a logarithm in base 3. Round to the nearest thousandth.
23. Solve .
24. Solve .
Write the expression as a single natural logarithm.
25.
26. The sales of lawn mowers t years after a particular model is introduced is given by the function y = , where y is the number of mowers sold. How many mowers will be sold 2 years after a model is introduced? Round the answer to the nearest whole number.
27. The generation time G for a particular bacteria is the time it takes for the population to double. The bacteria increase in population is shown by the formula , where t is the time period of the population increase, a is the number