Question

The average profit a local store owner earns on a given day is $550 and is growing exponentially at a rate of 60% per year. Write a function to represent profit after t years, where the daily 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 day, to the nearest hundredth of a percent.

Answer 1

The exponential function used to represent the profit after t years is $y=550(1.6)^t$

Exponential function

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y, and b is the multiplier.

Let y represent the profit after t years.

Since the profit on a given day is $550 and is growing exponentially at a rate of 60% per year. Hence:

• a = 550
• b = 100% + 50% = 1.6

The profit function is given by:

• $y=550(1.6)^t$

The exponential function used to represent the profit after t years is $y=550(1.6)^t$

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