Questions on Exponential Functions
Which of the following are exponential functions?
What is the domain of an exponential function f(x) = kb^{x}? 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.
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 strontium90 on the island was 100 times the level considered to be "safe" for human habitation. If the halflife of Strontium90 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.
