Question

In 2014 the population of Kenya was estimated to be 45,121,040 with a growth rate of 2.7%. Question 1 Use the exponential growth formula to write an equation that estimates the population y in terms of the time t. Enter your answer in the box. Then apply the exponential growth formula to estimate the population of Kenya in 2020. Round to the nearest whole number

Answer 1

To estimate the population of Kenya using the exponential growth formula, substitute the initial population and growth rate into the equation. Then, to estimate the population in 2020, substitute the year into the equation.

Step-by-step explanation:

To estimate the population of Kenya in terms of time using the exponential growth formula, we can use the equation: y = P(1 + r)t, where y is the estimated population at time t, P is the initial population, and r is the growth rate expressed as a decimal. In this case, the initial population P is 45,121,040 and the growth rate r is 2.7%, or 0.027 as a decimal. So the equation becomes:

y = 45,121,040(1 + 0.027)t

To estimate the population of Kenya in 2020, we substitute t = 2020 into the equation:

y = 45,121,040(1 + 0.027)2020

Calculating this expression will give us the estimated population of Kenya in 2020.

Answer 2

y = 45,121,040×1.027^t

Step-by-step explanation:

An exponential growth equation is generally of the form ...

value at time t = (initial value)(growth factor)^t

where the growth factor is the multiplier for a period equal to one time unit.

Here, the initial value (in 2014) is 45,121,040. The growth factor is given as 1.027 (2.7% added per year), and we can define t as the number of years after 2014. Then our equation is ...

y = 45,121,040×1.027^t . . . . where t = years after 2014