Exonential Growth Word Porblem

Question

Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 2200 bacteria selected from this population reached the size of

2372 bacteria in five hours. Find the hourly growth rate parameter. Note: This is a continuous exponential growth model. Write the answer as a percentage

Answer 1

The bacteria starts at a population of 2200. After every hour the population multiplies by some amount (The hourly growth rate parameter). Call this amount k.

After 1 hour, the population is 2200 * k.

After 2 hours, the population is 2200 * k * k

After 3 hours, the population is 2200 * k * k * k and so on.

Use this with the fact that the population is 2372 after five hours to solve for k.