APPLICATIONS OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS
(Population Word Problems)
To solve an exponential or logarithmic word problem, convert the narrative to an equation and solve the equation. In this section, we will review population problems.
Example 15: Convert the exponential equation
to an equivalent equation with base e.
Solution and Explanations:
Let's make a few observations before we begin. Since the base in the equation
is , and is less than 1, the value of f(t) will get smaller as the value of t gets larger.
When t = 0 at the start of study, f(t) = 50,000; therefore, 50,000 is the starting amount. We are going to find a few points that satisfy this equation and use these points to find the new equation.
When t = 0, the value of f(t) is 50,000, and the corresponding point is (0, 50,000). At t = 1, the value of f(t) is
At t = 2, the value of f(t) is
At t = 3, the value of f(t) is
The equation can now be written
rounded to 8,000. The model (equation) is correct.
We have just shown that the exponential equation
with base e is equivalent to the exponential equation
with base .
If you would like to work another example, click on Example
Author: Nancy Marcus