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 16: Convert the exponential equation

displaymath137

to an equivalent equation with A) base e, B) base 10, and C) base 23.

Solution and Explanations:

Let's make a few observations before we begin. Since the base is 1.12, greater than than 1, the value of f(t) will get larger as t gets larger. We are going to find a few points that satisfy this equation and use these points to find the new equations.

When t = 0, the value of f(t) is 5,000, and the corresponding point is (0, 50,000).

At t = 1, the value of f(t) is tex2html_wrap_inline155 , and the corresponding point is (1, 5,600).

At t = 2, the value of f(t) is tex2html_wrap_inline159 , and the corresponding point is (2, 6,272).

At t = 3, the value of f(t) is tex2html_wrap_inline163 , and the corresponding point is (23, 7,024.54).

Base e:

The equation

displaymath193

is equivalent to the equation

displaymath199

Observation: tex2html_wrap_inline201 , the original base.

Base 10:

The equation

displaymath237

is equivalent to

displaymath199

Observation: tex2html_wrap_inline241 , the original base.

Base 23:

The equation

displaymath269

is equivalent to the equation

displaymath199

Observation: tex2html_wrap_inline277 , the original base.

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

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Author: Nancy Marcus

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