Word problem

Question

A certain species of birds was introduced in a certain county 25 years ago. The
population doubles every 10 years, and now the population is 13,000.
a) What was the initial size of the population?
b) Estimate the population 5 years from now.

Answer 1

P(t) = P₀ (2)^t/10,

 

with t in years.

 

(a)

 

13,000 = P(25) = P₀ (2)^25/10 

 

13,000 = P₀ (2^2.5)

 

P₀ = 13,000 / 2^2.5 = 2298

 

(b)

 

P₀ is now 13,000.

 

P(5) = 13,000 (2)^5/10 = ?

 

You could also go back to the original population of 2298 and work this as

 

P(30) = 2298 (2)^30/10 = 2298 (2)³ = ?

 

They should give the same answer.