Question

Suppose that the number of bacteria in a certain population increases according to an exponential growth model, with a growth rate of 19% per hour. Suppose also that a sample culture of 2300 bacteria is obtained from this population. Find the size of the sample after five hours. Round your answer to the nearest integer.

Answer 1

Answer: 5489

Explanation:

Given the following :

Growth rate (r) = 19% per hour

Sample culture in population = 2300

Size of sample after 5 hours =?

Using the exponential relation:

P = Po * r^t

P = population after 5 hours

Po = Initial sample population

t = time

P = 2300 * (1 +19%)^t

P = 2300 ×(1 + 0.19) ^5

P = 2300 * 1.19^5

P = 2300 * 2.3863536599

P = 5488.61341777

P = 5489 (nearest integer)