Modeling with Mathematics The Population of a city has been incteasing by 2% ann

floymdiT

floymdiT

Answered question

2021-09-06

Modeling with Mathematics The Population of a city has been incteasing by 2% annually. The sign shown is from the year 2000.
a. Write an exponential growth function that represents the population t years after 2000.
b. What will the population be in 2020? Round your answer to the nearest thousand.

Answer & Explanation

nitruraviX

nitruraviX

Skilled2021-09-07Added 101 answers

a. Given: The population in the year 2000=315,000
Population growth rate =2% annually
Concept used:
Exponential growth function:
y=a(1+r)t ..... (1)
Here, the y is the final value, a is the initial value, and r is the rate of growth (in decimal form).
Calculation:
Substituting a=315,000 and r=0.02 in equation (1), the required exponential growth function is:
y=a(1+t)t
=315,000(1+0.02)t
=315,000(1.02)t
Conclusion:
So, the population t years after 2000 is given by the functiony=315,000(1.02)t.

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