# Calculus

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On the basis of data collected during an experiment, a biologist found that the growth of a fruit fly (Drisophila) with a limited food supply could be approximated by the exponential model below where t denotes the number of days since the beginning of the experiment.

(a) What was the initial fruit fly population in the experiment?
flies

(b) What was the maximum fruit fly population that could be expected under this laboratory condition?
flies

(c) What was the population of the fruit fly colony on the 14th day?
flies

(d) How fast was the population changing on the 14th day?
flies/day

• Calculus -

I don't see an "exponential model below" .

• Calculus -

N(t)= 600/1+24e^-0.21t

• Calculus -

I am sure you meant
n(t) = 600/(1 + 24e^-.21t )

a) let t=0, N(0) = 600/(1+24e^0) = 600/25 = 24

b) As t gets larger e^-.21t gets smaller
e.g. if t = 20, e^-4.2 = .015
so 24e^-.21t gets smaller
and our formula approaches 600/(1+0) = 600
so the maximum would be 600

c) sub in t=14
N(14) = 600/(1+24e^-2.94) = appr 264

d) N'(t) = -600(1+24e^-.21t)^-2 * 24(-.21)e^-.21t
sub in t=14

you do the button-pushing (I got 31)

• Calculus -

Thanks!

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