Question

The average profit a local store owner earns on a given day is $960 and is growing
exponentially at a rate of 88% per year. Write a function to represent profit after t
years, where the monthly rate of change can be found from a constant in the function.
Round all coefficients in the function to four decimal places. Also, determine the
percentage rate of change per month, to the nearest hundredth of a percent.

Answer 1

The average profit of the local store is an illustration of an exponential function

The profit function is: $y = 960 * (0.9894)^{x}$

How to determine the function

From the question, we have:

• Initial value (a) = 960
• Rate per year (b) = 88%

An exponential function is represented as:

$y = ab^x$

So, the function that represents the profit per year is:

$y = 960 * (88\%)^x$

Divide x by 12 to get the monthly rate

$y = 960 * (88\%)^{x/12}$

Evaluate the exponent

$y = 960 * (0.9894)^{x}$

Hence, the profit function is: $y = 960 * (0.9894)^{x}$

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