Answer:
The population will be 39400 in approximately 17 years
Step-by-step explanation:
The increase in population after t years is given by the formula
[tex]P_t = P_0(1+r)^t[/tex]
Here
P_0 is the initial population
r is the growth rate and t is time in years
So far we know,
P_0 = 20000
r = 4%
P_t = 39400
Putting the values in the formula
[tex]39400 = 20000(1+0.04)^t\\39400 =20000(1.04)^t\\\frac{39400}{20000} = (1.04)^t\\1.97 = (1.04)^t[/tex]
Taking natural log on both sides
[tex]ln |(1.04)^t| = ln |1.97|\\t\ ln\ |1.04| = ln\ |1.97|\\t = \frac{ln\ 1.97}{ln\ 1.04}\\t = 17.287\\t \approx 17[/tex]
Hence,
The population will be 39400 in approximately 17 years
