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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.

Question

contestada

Respuesta :

MrRoyal MrRoyal · Answer 1 · 2021-05-29T09:29:46+02:00

Answer:

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

Step-by-step explanation:

Given

[tex]y_1 = 10000(1.01)^x[/tex]

[tex]y_2 = 8000(1.02)^x[/tex]

Required

The population of each community after certain years.

[tex](a)\ x = 12[/tex]

We have:

[tex]y_1 = 10000(1.01)^x[/tex] [tex]y_2 = 8000(1.02)^x[/tex]

[tex]y_1 = 10000(1.01)^{12[/tex] [tex]y_2 = 8000(1.02)^{12[/tex]

[tex]y_1 = 11268.25[/tex] [tex]y_2 = 10145.93[/tex]

[tex]y_1 \approx 11300[/tex] [tex]y_2 \approx 10100[/tex]

[tex](b)\ x = 22[/tex]

We have:

[tex]y_1 = 10000(1.01)^{22[/tex] [tex]y_2 = 8000(1.02)^{22[/tex]

[tex]y_1 = 12447.158[/tex] [tex]y_2 = 12367.83[/tex]

[tex]y_1 \approx 12400[/tex] [tex]y_2 \approx 12400[/tex]

[tex](c)\ x = 16[/tex]

We have:

[tex]y_1 = 10000(1.01)^{16[/tex] [tex]y_2 = 8000(1.02)^{16[/tex]

[tex]y_1 = 11725.78[/tex] [tex]y_2 = 10982.28[/tex]

[tex]y_1 \approx 11700[/tex] [tex]y_2 \approx 11000[/tex]

[tex](d)\ x = 20[/tex]

We have:

[tex]y_1 = 10000(1.01)^{20[/tex] [tex]y_2 = 8000(1.02)^{20[/tex]

[tex]y_1 = 12201.90[/tex] [tex]y_2 = 11887.60[/tex]

[tex]y_1 \approx 12200[/tex] [tex]y_2 = 11900[/tex]