Question

A population of bacteria is growing according to the exponential model P = Cekt, where P is the number of colonies and t is measured in hours. If there are 800 colonies present after 4 hours, and the population's growth rate k = 0.65, how many colonies were present initially? [Round answer to the nearest hundredth.]

Answer 1

Plugging our values into the equation, we have


`800=Ce^(0.65(4)) \\ \\800=Ce^(2.6) \\\text{Dividing both sides by }e^(2.6) \\ \\(800)/(e^(2.6))=C \\ \\59.42=C`The correct answer is 59.42.