APPLICATIONS OF EXPONENTIAL AND
LOGARITHMIC FUNCTIONS

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

displaymath82

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

displaymath82

is tex2html_wrap_inline88 , and tex2html_wrap_inline88 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

displaymath108

At t = 2, the value of f(t) is

displaymath114

At t = 3, the value of f(t) is

displaymath120

We have just shown that the exponential equation

displaymath154

with base e is equivalent to the exponential equation

displaymath82

with base tex2html_wrap_inline88 .

If you would like to work another example, click on Example

[Menu Back to Solving Word Problems] [Menu Back Population Word Problems]

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Author: Nancy Marcus

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