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.

Problem 1: Find the equation to the base 2 that describes a population of cells that start with 5 cells and double every hour.

Solution and Explanations:

First record your observations by making a table with two columns: one column for the time and one column for the number of cells. The number of cells (population size) depends on the time. If you were to graph your findings, the points would be formed by (specific time, number of cells at the specific time). For example at t = 0, there are 5 cells, and the corresponding point is (0, 5). At t = 1, there are 10 cells, and the corresponding point is (1, 10). At t = 2, there are 20 cells, and the corresponding point is (2, 20). At t = 3, there are 40 cells, and the corresponding point is (3, 40).

You can see that the relationship between the two parts of the point is exponential where the exponent is the time. Therefore, we say that the equation that reflects the population growth of the cells is

Let's check it by estimating the population after 5 minutes with the formula and with the table. By the formula,

By the table, after 5 minutes the population is

Therefore the formula is

If you would like to work another problem, click on Problem

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