Question

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

Answer 1

To find when the population of two growing communities will be equal, we solve the given system of equations, we estimate the solution to be around 20 years, hence the correct option is D. 20.

Step-by-step explanation:

The subject of this question is Mathematics, specifically dealing with exponential growth equations. You need to solve the system of equations where two populations increase at different rates (1.01 and 1.02) to find the point in time (years), represented by x, when the populations are equal.

Using the system of equations:

• y = 10,000(1.01)^x
• y = 8,000(1.02)^x

By setting both equations equal to each other, we solve for the time:

10,000(1.01)^x = 8,000(1.02)^x

On simplifying, we estimate x as about 20 years. So, the answer is D. 20.

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