a. In 2000, the population of a country was approximately 5.53 million and 2084

Question

a. In 2000, the population of a country was approximately 5.53 million and 2084 it is projected to grow to 14 million. use the exponential growth model A=A(base 0)e^kt, in which t is the number of years after 2000 and A(base 0) is in millions, to find an exponential growth function that models data.

b. by which year will the population be 11 million?

a. type the exponential growth function that models the data is A=_____(simplify

your answer use integers or decimals for any number in the expression round to two decimal places as needed)

b. the country's population will be 11 million in the year ____( use the answer from part a to find this answer round to the nearest year as needed)

Explanation / Answer

Solution:

a)

lets take 2000 as t = 0

=> 2084 as t = 84

hence;

14 million = 5.53 million e^k(84)

=> e^k(84) = 14/5.53

taking ln at both sides:

=> 84k = 0.928869514

=> k = 0.011 (Approx.)

hence the exponential functio would simply be:

A = (5.53)e^(0.011)t {In millions}

b)

simply put A = 11 millions to find the time

=> 11 = 5.53 e^(0.011)t

=> t = 62.5188 years

i.e;

In 2063 the population of the town will be a little over 11 millions

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