The population of Adamsville grew from 9,000 to 17,000 in 6 years. Assuming uninhibited exponential​ growth, what is the expected population in an additional 5 ​years?

Question

The population of Adamsville grew from 9,000 to 17,000 in 6 years. Assuming uninhibited exponential​ growth, what is the expected population in an additional 5 ​years?

Answer 1

Assuming an equation like ab^t = P. where P = population. and t = time in years

Use the given situations to find a and b

At t = 0 , p=9000 ----> ab⁰ = 9000 ---> since b⁰ = 1, then a = 9000

Now we know 9000b^t = P. and we use our other given situation.

9000b⁶ = 17000 --->. b⁶ = 17000/9000 = 1.888...

then taking the 1/6 root of both sides ----> b = 1.1118 about

so 9000(1.1118)^t = P. Now find P when t = 11 since 6+5 = 11