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
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 , and the corresponding point is (1, 5,600).
At t = 2, the value of f(t) is , and the corresponding point is (2, 6,272).
At t = 3, the value of f(t) is , and the corresponding point is (23, 7,024.54).
Base e:
The equation can now be written
rounded to 0.11333.
The model (equation) is correct.
The equation
is equivalent to the equation
Observation: , the original base.
Base 10:
rounded to 0.0492.
This is close enough. Recall that it won't check exactly because we rounded the value of b.
The equation
is equivalent to
Observation: , the original base.
Base 23:
The equation can now be written
The equation
is equivalent to the equation
Observation: , the original base.
If you would like to work another example, click on Example
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Author: Nancy Marcus