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A salesperson increases the amount of sales, in dollars,each quarter by 15%. If the salesperson has $45,000 in sales in the 1st quarter, what is the
amount of total sales by the end of the 4th quarter, to the nearest cent?

Sagot :

Using an exponential function, it is found that the amount of total sales by the end of the 4th quarter is of $224,671.875.

What is an exponential function?

An increasing exponential function is modeled by:

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

In which:

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

In this problem, the parameters are r = 0.15 and A(0) = 45000.

Then:

  • For the first quarter, A(0) = 45000.
  • For the second, A(1) = 45000(1.15) = 51720.
  • For the third quarter, A(2) = 45000(1.15)² = 59512.5.
  • For the fourth quarter, A(3) = 45000(1.15)³ = 68439.375

Then, the total amount is:

T = A(0) + A(1) + A(2) + A(3) = 45000 + 51720 + 59512.5 + 68439.375 = $224,671.875.

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

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