This exercise uses the population growth model.

Question

A certain species of bird was introduced in a certain county 25 years ago. Biologists observe that the population doubles every 10 years, and now the population is 24,000.

(a) What was the initial size of the bird population? (Round your answer to the nearest whole number.)

(b) Estimate the bird population 9 years from now. (Round your answer to the nearest whole number.)

 birds

Answer 1

I disagree with Mark's answer. My answer is as follows.

Let P be birds population after y years and Pi is initial population then according to condition

P = Pi (a) ^y, here a is growth factor. Since population doubles after 10 years

P/Pi = 2 = a^10, Solve for a = 1.071778463

Now it is given that population after 25 years = 24000 Therefore

24000 = Pi (1.071773463)^25 Solve Pi = 4242.64 ≅ 4243 Initial population = 4243

Population 9 years from now that is 34 years from start time

P = 4242.64 X (1.071773463)^34 = 44785.577 = 44786 I hope this helps.

Shailesh K., Senior Math and Physics Instructor

Answer 2

24000 = a₀(2)^25/10

24000 ≈ a₀2.828427125

8485.28 = a₀

a₉ = 8485(2)^9/10