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
