1. Solve the following using the same base method.Show work.

1. 13^{(x + 11)}= 13⁸

2. 4^x= 16

3. 2^{(3x - 6)}= 8

4. 5^{(- 3x)}= 1/25

B.Solve the following using logarithms.Show all steps.

5. 3^x= 29

6. 8(3^{x - 6}) = 876

7. 5e^{(2.1x - 2)}= 14

C.Solve the following exponential word problems.Show all steps.

8. A biologist is researching a newly-discovered species of bacteria. At timet= 0 hours, he puts seventy-five bacteria into what he has determined to be a favorable growth medium. Four hours later, he measures 325 bacteria. Assuming exponential growth, what is the growth constant "k" for the bacteria? (Roundkto two decimal places.)

9. The half-life of a radioactive substance is one hundred twenty-five days. How many days will it take for eighty-two percent of the substance to decay?

D. SAT/ACT problemShow your work to verify your answer.

10. A researcher estimates that the population of a city is increasing at an annual rate of 0.6%. If the current population of the city is 80,000, which of the following expressions appropriately models the population of the city t years from now according to the researcher's estimate?

A) 80,000(1 + 0.006)t

B) 80,000(1 + 0.006t )

C) 80,000 + 1.006t

D) 80,000(0.006t )