Question

On the basis of data collected during an experiment, a biologist found that the growth of a fruit fly population (Drosophila) with a limited food supply could be approximated by
N(t) = 600/1+39e^-0.16t
(a) What was the initial fruit fly population in the experiment? where t denotes the number of days since the beginning of the experiment.
(b) What was the population of the fruit fly colony on the t = 11 day? (Round your answer to the nearest integer.)

Answer 1

Answer:

(a). 15

(b). 78

Step-by-step explanation:

Growth of the population of a fruit fly is modeled by

N(t) = $\frac{600}{1+39e^{-0.16t} }$

where t = number of days from the beginning of the experiment.

(a). For t = 0 [Initial population]

N(0) = $\frac{600}{1+39e^{-0.16\times 0} }$

       = $\frac{600}{1+39}$

       = $\frac{600}{40}$

       = 15

Initial population of the fruit flies were 15.

(b).Population of the fruit fly colony on 11th day.

N(11) = $\frac{600}{1+39e^{-0.16\times 11} }$

       = $\frac{600}{1+39e^{-1.76} }$

       = $\frac{600}{1+39\times 0.172 }$

       = $\frac{600}{1+6.71}$

       = $\frac{600}{7.71}$

       = 77.82

       ≈ 78

On 11th day number of fruit flies colony were 78.