The population of a certain country since January 1, 1910 can be approximated by the model below, where tt is the number of years since January 1, 1910.

Question

The population of a certain country since January 1, 1910 can be approximated by the model below, where t is the number of years since January 1, 1910.

P(t)=56.58 / 1 + 7.2e^-0.02706t

where P is the population of this country (in millions) ttyears after January 1, 1910.

(a) What was the population of this country on January 1, 1910?

____________ million

(b) Use the function to approximate the population of this country on January 1, 1927. Round your answer to the nearest whole number.

____________ million

(c) In what year will the population reach 21 million? Round your answer to the nearest year.

____________ year

Answer 1

So the original equation is P(t)=56.58 / 1+7.2e^-0.02706t

a) The population of this country on January 1, 1910 is:

=> P(t=0)=56.58 / 1+7.2e^-0.02706(0)

=> 6.9 million.

b) the population of this country on January 1, 1927 :

t=1927-1910=17 years

=> P(t=17)=56.58 / 1+7.2e^-0.02706(17)

=> 10.2

Therefore the population on January 1, 1927 will be: 10.2 million.

c)the year in which the population will reach 21 million is:

P(t)=56.58 / 1+7.2e^-0.02706t

P(t)= 21

21= 56.58 / 1+7.2e^-0.02706t

Then you solve for t using any method (logarithm being the best one):

t= 53.46 years => 53 years

Therefore it will take 53 years for the population to reach 21 million

Therefore the population will reach 21 million in the year: 1963 .

Hope this helped you dear student!!