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Brandon is analyzing the profits from two of his restaurant locations. the first location showed a profit of $3,000 in the first week of the year but has a showed a steady decrease in profits of 1.5% each week since then. his second location showed a profit of $1,500 in the first week of the year and has showed a steady increase in profits of 1.2% each week since then. which system of equations can brandon use to determine the number of weeks, x, until the profits, y, from the two locations are the same? a. b. c. d.

Respuesta :

The system of exponential functions that can be used to determine the time for the profits to be the same is given by:

[tex]3000(0.985)^x = 1500(1.012)^x[/tex]

What is an exponential function?

An exponential function is modeled by:

[tex]A(t) = A(0)(1 \pm r)^t[/tex]

In which:

  • A(0) is the initial value.
  • r is the rate of change, as a decimal.

For the first restaurant, we have that the parameters are given as follows:

A(0) = 3000, r = -0.015.

Hence the profit after x weeks is given by:

[tex]y_1(x) = 3000(0.985)^x[/tex]

For the second restaurant, we have that:
A(0) = 1500, r = 0.012.

Hence:

[tex]y_2(x) = 1500(1.012)^x[/tex]

Then they will be equal when:

[tex]y_1(x) = y_2(x)[/tex]

[tex]3000(0.985)^x = 1500(1.012)^x[/tex]

More can be learned about exponential functions at https://brainly.com/question/25537936

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