Section 5.5 Applications of Exponential and Logarithmic Functions

Section Objectives

Solve application problems involving exponential and logarithmic equations.

Determine an exponential or logarithmic model for a problem situation.

Examples

In a research experiment, a population of fruit flies is growing exponentially. After 2 days there are 100 flies, and after 4 days there are 300 flies. Find a model of the form that describes the population at time . How many flies will there be after 5 days?

When using carbon-14 dating, scientists use the formula , where is the ratio of carbon-14 to carbon-12 years after death. Estimate the age of an organic object for which the ratio of carbon-14 to carbon-12 is .

Plutonium-239 has a half-life of about 24,100 years. Use a model of the form to determine the initial amount of Pu-239 if there were 0.4 grams remaining after 1000 years.

One-hundred animals were released into a preserve were their population grows according to the model , where is measured in months. After how long will the population reach 750 animals?