20. On the basis of data collected during an experiment, a biologist found that

Question

20. On the basis of data collected during an experiment, a biologist found that the growth of the fruit fly (Drosophila) with a limited food supply could be approximated by the exponential model NU) 400 L+39e-0ISt where / denotes the number of days since the beginning of the experiment. What was the initial fruit fly population in the experiment? What was the maximum fruit fly population that could be expected under this laboratory condition? What was the population of the fruit fly colony on the 20th day? Please give the answer as an integer How fast was the population changing on the 20th day? Please give the answer as an integer.

Explanation / Answer

N(t) = 400/(1+39e^(-0.15t))

For initial, plug in t =0

N(0) = 400/(1+39e^(-0.15*0)) = 400/(1+39) = 10 fruit fly

----------

For maximum, t-> inf

= 400/(1+39*0) = 400/1 = 400 fruit fly

-------------

For 20th day, plug in t =20

N(20) = 400/(1+39e^(-0.15*20)) = 135.97 = 136 fruit fly

----------

N'(t) = 2340e^(0.15t)/(e^(0.15t)+39)^2

plug in t=20

N'(t) = 2340e^(0.15*20)/(e^(0.15*20)+39)^2

13 fruit fly per day

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.