Answer:
(a). 15
(b). 78
Step-by-step explanation:
Growth of the population of a fruit fly is modeled by
N(t) = [tex]\frac{600}{1+39e^{-0.16t} }[/tex]
where t = number of days from the beginning of the experiment.
(a). For t = 0 [Initial population]
N(0) = [tex]\frac{600}{1+39e^{-0.16\times 0} }[/tex]
= [tex]\frac{600}{1+39}[/tex]
= [tex]\frac{600}{40}[/tex]
= 15
Initial population of the fruit flies were 15.
(b).Population of the fruit fly colony on 11th day.
N(11) = [tex]\frac{600}{1+39e^{-0.16\times 11} }[/tex]
= [tex]\frac{600}{1+39e^{-1.76} }[/tex]
= [tex]\frac{600}{1+39\times 0.172 }[/tex]
= [tex]\frac{600}{1+6.71}[/tex]
= [tex]\frac{600}{7.71}[/tex]
= 77.82
≈ 78
On 11th day number of fruit flies colony were 78.
