Question

Select the correct answer from each drop-down menu.

City officials use the given system of equations to estimate the population of two neighboring communities, where y is the population and x is

the time, in years.

y = 10,000(1.01)

y = 8,000(1.02)

Use this system to complete the statement.

After about _______

A.12

B.22

C.16

D.20

years, the population of each community will be approximately_____

A.18,270

B.14,400

C.16,200

D.11,300

people.

Answer 1

After about 22 years, the population of each community will be approximately 12400

Explanation:

Given

`y_1 = 10000(1.01)^x`

`y_2 = 8000(1.02)^x`

Required

The population of each community after certain years.

`(a)\ x = 12`

We have:

`y_1 = 10000(1.01)^x`
`y_2 = 8000(1.02)^x`

`y_1 = 10000(1.01)^{12`
`y_2 = 8000(1.02)^{12`

`y_1 = 11268.25`
`y_2 = 10145.93`

`y_1 \approx 11300`
`y_2 \approx 10100`

`(b)\ x = 22`

We have:

`y_1 = 10000(1.01)^{22`
`y_2 = 8000(1.02)^{22`

`y_1 = 12447.158`
`y_2 = 12367.83`

`y_1 \approx 12400`
`y_2 \approx 12400`

`(c)\ x = 16`

We have:

`y_1 = 10000(1.01)^{16`
`y_2 = 8000(1.02)^{16`

`y_1 = 11725.78`
`y_2 = 10982.28`

`y_1 \approx 11700`
`y_2 \approx 11000`

`(d)\ x = 20`

We have:

`y_1 = 10000(1.01)^{20`
`y_2 = 8000(1.02)^{20`

`y_1 = 12201.90`
`y_2 = 11887.60`

`y_1 \approx 12200`
`y_2 = 11900`