Question

In a lab, 180 cells are present at the beginning of an experiment. During the first 9 hours, the number of cells increased by 8% each hour. Write an exponential model giving the number of cells y present t hours after starting the experiment. Estimate the time when the number of cells is 360.

Answer 1

The answer is 9 hours

Explanation:

From the initial population of 180 cells, the number grows by 8% every hour for the first 9 hours.

This represents a increased population of 108% the previous population.

108% = 108/100 = 1.08

So the new population after n hours is

180 x 1.08^n

When population is 360

360 = 180 x 1.08^n

1.08^n = 2

Take log of both sides

n x Log1.08 = Log 2

n = Log 2/Log 1.08

n = 9