What is the answer

Question

A biologist is conducting an experiment that involves a colony of fruit flies. (Biologists frequently study fruit flies because their short life span allows the experimenters to easily study several generations.) One day, there were 2,730 flies in the colony. Three days later, there were 5,880.

(a) Develop the mathematical model that represents the population p of flies. (Write your model in terms of t, where t is measured in days. Round the coefficient of t to seven decimal places.)

p(t) = 

(b) Use the model to predict the population after one week. (Round your answer up to the next whole number.)

(c) Use the model to predict when the population will be double its

Answer 1

A biologist is conducting an experiment that involves a colony of fruit flies.

One day, there were 2,730 flies in the colony. Three days later, there were 5,880.

Given: Start 2730 Flies, 3 days later 5880 flies

(a) Develop the mathematical model that represents the population p of flies. (Write your model in terms of t, where t is measured in days. Round the coefficient of t to seven decimal places.)

let p₀= initial population

k = constant that depends on the rate of growth

t = time

p(t) = p₀e^kt

To determine the value of k to 7 decimal places

Use 2730 as your initial population, 5880 is your population after t=3 days

5880 = 2730 e^k(3)

3k = ln(5880/2730)

k = 0.2557517

So our equation is

p(t) =2730e^(0.2557517)t

(b) Use the model to predict the population after one week. (Round your answer up to the next whole number.)

1 week = 7 days. Substitute 7 for t

p(t) =2730e^(0.2557517)t

p(7) =2730e^(0.2557517)7

p(7) = 16355 flies

(c) Use the model to predict when the population will be double its

p(double) = 2 x p₀

2p₀ = p₀e^(0.2557517)t

2 = e^(0.2557517)t

t = [ln 2] / 0.2557517

t = 2.71 days

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