Question

Exponential Model: P(t) = M(1 − e^−kt) where M is maximum population.

Logistic Model: P (t) = M / 1+Be^−MKt where M is maximum population.

Scientists study a fruit fly population in the lab. They estimate that their container can hold a maximum of 500 flies. Seven days after they start their experiment, they count 250 flies.

1. (a) Use the exponential model to find a function P(t) for the number of flies t days after the start of the experiment.

(b) Use your function to estimate how many flies there will be after 14 days.

(c) Use your function to estimate when there will be 490 flies.

2. Supposing that the experiment began with 50 flies, use the logistic model (and the same information from the previous problem) to find a different function for P(t). Note that the K in the Logistic formula is not the same as the k from the Exponential Formula.

(a) Use this new function to estimate how many flies there will be after 14 days.

(b) Use your function to estimate when when there will be 490 flies.

3. Which model do you think does a better job of modeling the growth of the fruit fly population? Explain why you think this.

Answer 1

(3) Logistic model acts a feed back model that is as the populations grows the rate of change of population decreases. Exponential model starts with zero population at time zero which is not practical as population of flies cannot grow from zero. Hence logistic model better.