Question

The population of a country on January 1, 2000, is 20.7 million and on January 1, 2010, it has risen to 22.6 million. Write a function of the form P(t)

Answer 1

Answer:

P(t) = 20.7e^0.0087816t

Step-by-step explanation:

Given that :

Initial population ; Jan 1, 2000 = 20.7 million

Current population ; Jan, 2010 = 22.6 million

A function of the form P(t)

Where t = time

Usingbthe exponential growth function :

P(t) = Poe^rt ;

P(t) = population at a time after the initial population figure

Po = initial population

r = growth rate

t = time in years

P(t) = population in 2010 = 22.6 million

Po = population in 2000 = 20.7 million

t = 10 years

22.6 = 20.7e^r * 10

22.6 = 20.7e^10r

22.6 / 20.7 = e^10r

1.0917874 = e^10r

Take the In of both sides

In(1.0917874) = 1n(e^10r)

0.0878162 = 10r

r = 0.0878162 / 10

r = 0.0087816

Hence,

P(t) = 20.7e^0.0087816t