Question

The population of a certain colony of bacteria increases by 3% each hour. After 7 hours, what is the percent increase in the population over the initial population? The percent increase is (Round to the nearest integer as needed.)

Answer 1

To calculate the percent increase in the population over the initial population after 7 hours, we use the formula for exponential growth. The percent increase is approximately 22.5%.

Step-by-step explanation:

To calculate the percent increase in the population over the initial population, we need to use the formula for exponential growth. The formula is:

New Population = Initial Population * (1 + Growth Rate)^Time

In this case, the growth rate is 3% per hour, so the formula becomes:

New Population = Initial Population * (1 + 0.03)^7

Let's say the initial population is 100. Plugging in the values, we get:

New Population = 100 * (1 + 0.03)^7

New Population = 100 * (1.03)^7

New Population = 100 * 1.2250436

New Population = 122.50436

The percent increase in the population is given by:

Percent Increase = (New Population - Initial Population) / Initial Population * 100

Plugging in the values, we get:

Percent Increase = (122.50436 - 100) / 100 * 100

Percent Increase = 22.50436%

So, the percent increase in the population over the initial population after 7 hours is approximately 22.5%.