When Richard moved to Clover Hills one year ago, it had a population of 3,650 . Today, the
population has increased to 3,869 , and it is expected that the population will continue to
increase each year.
Write an exponential equation in the form that can model the Clover Hills
population, years after Richard moved there.
Use whole numbers, decimals, or simplified fractions for the values of and .

To the nearest hundred people, what can Richard expect the population to be 4 years after he
moved there?
people

Ask by Ortiz Hall. in the United States

Mar 24,2025

Question

When Richard moved to Clover Hills one year ago, it had a population of 3,650 . Today, the
population has increased to 3,869 , and it is expected that the population will continue to
increase each year.
Write an exponential equation in the form that can model the Clover Hills
population, years after Richard moved there.
Use whole numbers, decimals, or simplified fractions for the values of and .

To the nearest hundred people, what can Richard expect the population to be 4 years after he
moved there?
people

Ask by Ortiz Hall. in the United States

Mar 24,2025

UpStudy AI · Accepted Answer

Given that the initial population is $$3650$$ (when $$x=0$$) and after 1 year the population is $$3869$$, we can write:

$$
3650\cdot b = 3869
$$

To find $$b$$, divide both sides by $$3650$$:

$$
b = \frac{3869}{3650} = 1.06
$$

Thus, the exponential equation modeling the population is:

$$
y = 3650(1.06)^x
$$

To find the population 4 years after Richard moved, substitute $$x = 4$$:

$$
y = 3650(1.06)^4
$$

Calculate $$(1.06)^4$$:

$$
(1.06)^4 \approx 1.2625
$$

Now multiply by $$3650$$:

$$
y \approx 3650 \times 1.2625 \approx 4609
$$

Rounding $$4609$$ to the nearest hundred gives:

$$
4600 \text{ people}
$$

Thus, to the nearest hundred people, the population is expected to be $$4600$$ after 4 years.
The exponential equation modeling the population is $$ y = 3650(1.06)^x $$. After 4 years, the population is expected to be approximately 4600 people.

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