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1. Write an equation that defines the exponential function with base a > 0.

(b) What is the domain of this function?

(c) If a cannot = 1 what is the range of this function.

2. Starting with the graph y = e^x, write the equation of the graph that results from the following changes.

3. Consider the graph of y = e^x

(a) Find the equation of the graph that results from reflecting about the line y = 5.

(b)Find the equation of the graph that results from reflecting about the line x = 4.

4. Find the domain of each function. (Enter your answer using interval notation.)

(a) f(x) = (16 – e^x^2)/(1- e^16-x^2)

(b) f(x) = (8 + x)/(e^cosx)

5. Find the domain of each function. (Enter your answer in interval notation.)

(a) g(t) = sin(e^-t)

(b) g(t) = sqrt(1 – 2^t)

6. Find the exponential function f(x) = Ca^x whose graph is given.

7. Find the limit. Lim x infinity(e^-4x cos x)

8. Use the Law of Exponents to rewrite and simplify the expression.

(a) (9^-3)/(3^-8)

(b) 1/(x^4)^1/3

9. Use the Law of Exponents to rewrite and simplify the expression.

(a) b^8 (2b)^7

(b) (6y^3)^4/(2y^7)

10. A bacteria starts with 700 bacteria and doubles in size every half an hour.

(a) How many bacteria are there in 4 hours?

(b) How many bacteria are there after t hours?

(c) How many bacteria are there after 40 minutes?

(d) Graph the population function.

Estimate the time for the population to reach 10,000.