An analyst studying the population of a town determines that the population can be modeled by the formula f(t)=120,000(1.015)t , where f(t) represents the population after t years.
A city council member makes this claim:
“Based on the formula, after 1 year the population will have increased by 1,800. Since 2,800 divided by 12 is 150, we can use the fact that the population increased by 150 people per month to predict the future population of the town”.

Part A: Explain why the city council member’s claim is or is not a valid way to predict the population.

Part B: Modify the initial given formula such that it represents the predicted population by month.

Part C: What is the population after 50 months?

A.The city council member's claim is not valid because according to the formula, t is in years, so it has to be divided by 12 months then multiplied by 1.015

B. f(t)=120,000 (1.015)t/12 where the t is time in years is divided by 12 to get time in months

C. 507500 people

Step-by-step explanation:

Given that the population can be modeled by the formula f(t)=120,000(1.015)t , where f(t) represents the population after t years.

Based on the formula, after 1 year the population will be;

f(1)=120,000(1.015)1

=120,000*1.015

=121,800

The city council member's claim is not valid because according to the formula, t is in years, so it has to be divided by 12 months then multiplied by 1.015

B.

The formula can be modified as;

f(t)=120,000 (1.015)t/12 where the t is time in years is divided by 12 to get time in months

C.

The population after 50 months will be;

f(t)=120,000 +(1.015)t/12

f(50/12) =120,000(1.015)*50/12

=120,000(1.015) * 4.167

=507500

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tallinn tallinn · Answer 2 · 2025-03-24T23:37:44-04:00

A. The city council member’s claim is not a valid way to predict the population is 121,800

B. f(t)=120,000 (1.015)t/12 to get time in month

C. 507500 people

Calculation of Population

A. Given that information as per the question, the population can be modeled by the formula f(t)=120,000(1.015)t, where f(t) represents the population after t years.

It is Based on the formula, after 1 year the population will be;

Then, f(1)=120,000(1.015)1

After that, =120,000*1.015

Thus, =121,800

Hence, The city council member's claim is not valid because according to the formula, t is in years, Also, it has to be divided by 12 months then multiplied by 1.015

B. Using The formula can be modified as;

Therefore, f(t)=120,000 (1.015)t/12 where the t is time in years is divided by 12 to get time in months

C. When The population after 50 months will be;

Then, f(t) is =120,000 +(1.015)t/12

After that, f(50/12) =120,000(1.015)*50/12

Now, =120,000(1.015) * 4.167

Thus, =507500

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