Approximately how many years will it take for the population to reach 300 million?

Question

The population of a country in million of residents is modeled by f(t)=256.12e^0.0054t

Answer 1

Set f(t) = 300 and solve for t.  I assume t = years from the moment the population was 256.12 million.

 

300 = 256.12 e^0.0054t ⇒ 

 

t = ln(300/256.12) / 0.0054 ≅ 29.285 years

 

Test the answer.

Answer 2

Set f(t)=300

 

300 = 256.12e^0.0054t

 

 

Divide both sides of the equation by 256.12

 

1.1713 = e^0.0054t

 

 

Log both sides of the equation.

 

ln(1.1713) = 0.0054t lne

 

ln(1.1713) = 0.0054t

 

 

Now you can solve for t.