Solve the given problem related to population growth. During the first decade of this century the population of a certain city grew exponentially the

avissidep

avissidep

Answered question

2021-01-16

Solve the given problem related to population growth.
During the first decade of this century the population of a certain city grew exponentially the population of the city was 146210 in 2000 and 217245 in 2010. Find the exponential growth function that models the population growth of the city use t= 0 to represent 2000 and t= 10 to represent 2010 and so on.
N(t)=?
Use your exponential growth function to predict the population of the city in 2016. Round to the nearest thousand.

Answer & Explanation

Gennenzip

Gennenzip

Skilled2021-01-17Added 96 answers

Let the exponential growth function is, N(t)=N0ekt
where N0 and k are the arbitrary constant and t is time.
Since it is given that at t=0 the population of the city was 146,210 so,
146210=N0ek(0)
N0=146,210
Also it is given that the population of the city was 217,245 at t=10. so,
217245=146210ek(10)
10k=217245146210
10k=ln(1.4858)
k=0.03959
Hence, the exponential growth function will be, N(t)=146210e0.03959t
Substitute t=1 to find the population in the year 2016,
N(16)=146210e0.03959(16)
=146210e0.6335
=146210×1.884
=275460
Hence, the population of the city will be 275,460 in 2016.

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