A logistic population growth problem using the Example 5 differential equation m

Question

A logistic population growth problem using the Example 5 differential equation model. Assume 50 fruit flies (P0 = 50) are in a large jar at the beginning (t = 0) of an experiment. Let P[t) be the number of fruit flies in the ja rt days later. At first, the population grows exponentially, but due to limited space and food supply, the growth rate decreases and the population growth rate and approaches the carry capacity of M = 300 . This experiment can be modeled by the Example 5 differential equation dp / dt = Kp(1 - p / M) with K = 0.1 and M = 300. The Example 5 gives the Formula (7) on Page 360 as the solution of dP / dt = KP(1 - p / m). By using the given values of P0, k and M and Formula (7) on Pag beginning. Show your result in whole number.

Explanation / Answer

A=(M-Po)/Po

A=(300-50)/50

A=5

P(t)=M/(1+ Ae-kt)

k=0.1,t=20

P(20)=300/(1+ 5e-0.1*20)

P(20)=300/(1+ 5e-2)

P(20)=300/(1+ 5e-2)

20 days after the begining,number of fruit fliers P(20)=179

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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