Question

Match each function to its domain and range.

a country's population in 1990 was 37 million in 1999 it was 40 million estimate the population in 2016 using exponential growth formula round your answer to the nearest million



Domain and Range
Function
domain: {0, 1, 3, 5, 6}
range: {-20, -16, -8, 0, 4}
arrowBoth
domain: {-2, -1, 0, 3, 4}
range: {-13, -8, -3, 12, 17}
arrowBoth
domain: {-4, -2, 0, 2, 4}
range: {-40, -20, 0, 20, 40}
arrowBoth
domain: {-3, -2, -1, 2, 6}
range: {0.5, 0, -1.5, 3, 2}
arrowBoth

Answer 1

This is the concept of application of exponential growth, suppose in 1990 time,t=0 and in 1990 time,t=9. Using the exponential growth formula given by:

f(t)=ae^(kt)

thus substituting the value we get:

40=37e^(9k)

this can be written as:

(40/37)=e^(9k)

introducing the natural logs we get:

ln(40/37)=9k

hence;

k=1/9ln(40/37)=0.0087

Therefore our formual will be given by:

f(t)=37e^(0.0087t)

N/B: The population is in millions. Thus to get the population in 2016 we shall proceed as follows;

t=26

thus

f(t)=37e^(26*0.0087)

f(t)=46.35 million

Explanation: