4.If the rate of growth of the weasel population in Problem 3 was 5% instead of

Question

4.If the rate of growth of the weasel population in Problem 3 was 5% instead of 3%, how many years would it take for the population to double?

"3. A population of weasels is growing at rate of 3% per year. Let wn be the number of weasels n years from now and suppose that there are currently 350 weasels. (a) Write a difference equation which describes how the population changes from year to year. (b) Solve the difference equation of part (a). If the population growth continues at the rate of 3%, how many weasels will there be 15 years from now? (c) Plot wn versus n for n = 0, 1, 2, . . . , 100. (d) How many years will it take for the population to double? (e) Find limn wn. What does this say about the long-term size of the population? Will this really happen?"

Explanation / Answer

Let " P" denotes the weasel population as of now and " T " be the time period it takes to reach the population to double.

Population growth rate is given as 5% = 5/100 = .05

2 * P = P * e ^ 0.05 T

2 = e^0.05 T

Log (2) = 0.05T that means T = Log (2) / 0.05 = .6931/0.05 = 13.86294

With a growth rate of 5% , It takes 13.86 years to reach the weasel population to double

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

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