# 3.1

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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.