Questions on Exponential Functions

What's On This Page

This page contains sample problems on exponential functions. They are for Self-assessment and Review.

Each problem (or group of problems) has an "answer button" ANSWER which you can click to look at an answer. Some solutions have a "further explanation button" Explain which you can click to see a more complete, detailed solution.

What to Do

To gain the most benefit from these problems,

Work the problems on your own. Write down your solutions BEFORE looking at any answers.

Use a graphing calculator as appropriate. A graphing calculator can be used to verify that your answers "make sense" or "look right".

If you have difficulties with this material, please contact your instructor. (See Getting Help in Stage 1.) You will need to get up to speed on exponential functions IN ADDITION to learing the material in the first few Stages.

Which of the following are exponential functions?

  1. f(x) = 3e-2 x

  2. g(x) = 2x/2

  3. h(x) = x3/2

  4. g(x) = 15 / 7x


What is the domain of an exponential function f(x) = kbx? What is the range? Describe the shape of the graph for b > 1, and for b < 1. What happens to f(x) in each case when x becomes very large (increases without bound) and as x becomes very small (decreases without bound)? Are there any horizontal asymptotes?


Solve the following equations. You should not need to use logarithms for the first three.

  1. 2x = 32

  2. 5x = 1/125

  3. (1/3)2x = 243

  4. 45 = 53x

  5. 500 = 1000e-.75 x

  6. 56 = 14(1 + e.195 x)


The population of bacteria in a culture is growing exponentially. At 12:00 there were 80 bacteria present and by 4:00 PM there were 500 bacteria. Find an exponential function f(t) = ke at that models this growth, and use it to predict the size of the population at 8:00 PM.


The last nuclear test explosion was carried out by the French on an island in the south Pacific in 1996. Immediately after the explosion, the level of strontium-90 on the island was 100 times the level considered to be "safe" for human habitation. If the half-life of Strontium-90 is 28 years, how long will it take for the island to once again be habitable?

Hint: Find an exponential decay model (function) for this situation.


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