Question

In 2000, the population of Big Springs was 13 thousand. Use the given doubling

time to predict the population in 2100. Assume a doubling time of 40 years.

Answer 1

The answer is "26179.4".

Explanation:

Assume year 2000 as t, that is t =0.

Formula:

`A= A_0e^(rt)`

Where,

`A_0 = \ initial \ pop \\\\r= \ rate \ in \ decimal \\\\t= \ time \ in \ year`

for doubling time,

`r = (log (2))/(t) \\`

`r = (\log (2))/( 40) \\\\r= (0.301)/(40)\\\\r= 0.007`

Given value:

`A = A_0e^(rt) \\\\`

`A_0 = 13000`

`t= 40 \ years`

when year is 2000, t=0 so, year is 2100 year as t = 100.

`A = 13000 * e^(et)\\\\A = 13000 * e^(e * t)\\\\A = 13000 * e^(0.007 * 100)\\\\A = 13000 * e^(0.7)\\\\A= 13000* 2.0138\\\\A = 26179.4`