Question

A boat's value over time is given as the function f(x) and graphed below. Use A(x) = 400(b)x + 0 as the parent function. Which graph shows the boat's value increasing at a rate of 25% per year?

Answer 1

The answer is the graph shown bellow

Explanation:

I took the quiz

Answer 2

A graph that shows the boat's value increasing at a rate of 25% per year is: D. graph D.

In Mathematics and Statistics, a population or material that increases at a specific period of time represents an exponential growth.

This ultimately implies that, a mathematical model for any population or material that increases by "b" percent per unit of time is an exponential function of this form:

`A(x) = P(1 + b)^(x)`

Where:

• A(x) represents the future value.
• P represents the initial value.
• b represents the rate of change or growth rate.
• x represents the time.

Since the boat's value is increasing at a rate of 25% per year, we can reasonably infer and logically deduce that its growth rate is as follows;

Growth rate, b = 1 + (25/100)

Growth rate, b = 1.25

By using the parent function, the required exponential growth rate function is given by;

`A(x) = 400(b)^x + 0\\\\A(x) = 400(1.25)^x`

In conclusion, only graph D correctly show a boat's value that is increasing at a rate of 25% per year.