How would I calculate growth rate?

Question

The population in Nigeria has been growing exponentially at a continuous rate. On January 01, 2000, the population was 110 million. On January 01, 2010, the population was 158 million.

 

(a) Determine the growth rate for the population of Nigeria. Your answer must be exact, that is, symbolic (NO decimal places anywhere).

Answer 1

Let P(t) = population (in millions) t years after Jan 1, 2000

 

P(t) = 110e^kt, where k is the growth rate

 

P(10) = 110e^10k = 158

 

                e^10k = 158/110 = 79/55

 

                  10k = ln(79/55)

 

                     k = (1/10)ln(79/55)