(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 2: Find the equation to the base 4 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 twice as many cells or 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).
Let's start with the generic exponential function with a base equal to 4
where a is the size of the population (number of cells) at the beginning of the student, t equals time into the study, and f(t) is the population at time t.
The correct answer is
If you would like to work another problem, click on Problem
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Author: Nancy Marcus