Exponential Functions and their Graphs
1. Use a calculator to evaluate the expressions and express the answer to six decimal place accuracy.
| a) | |
b) | |
c) | |
d) | |
2. Use properties of exponents to determine which of the following are equal.
| a) | f(x) = 23x - 2 | b) | g(x) = 23x - 4 | c) |  |
3. Use properties of exponents to solve the exponential equation stated below.
33x-2 = 95x + 7 . {Hint: Begin by rewriting the right hand side using a base of 3}
4. The graph shown below with the heavy line is the graph of y = ax with 2< a < 3.
Match each of the exponential functions listed
below with its corresponding graph.
Suggestion: Consider transformations of the graph y = ax .
| a) | y = a- x | b) | y = ax -1 | c) | y = - ax | d) | y = (1+a)x |
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| (i) | (ii) | (iii) | (iv) |
5. Bacterial growth: A population of bacteria in a culture increases according to the model P(t) = 725e .023 t where t is measured in hours and t = 0 corresponds to 7:00 am.
i) Use this model to estimate the number of bacteria at 8:30 am.
ii)Use this model to estimate the number of bacteria at 9:00 pm.
iii) Sketch the graph of P for 0 < t < 20 .
6. Radioactive decay: Suppose that a radioactive isotope has a half-life of 5 days. If there are 200 milligrams at t = 0 and if the amount A(t) remaining after t days is given by A(t) = 200 e - (.139 t) , then
i) find amount remaining after
8 days
ii) sketch the graph of the function A for 0
< t < 20
iii) using the graph, approximate the number of
days elapsed until only 75 milligrams remain.