Question

The number of members f(x) in Joe's health club increased by 25% every year over a period of x years. The function below shows the relationship between f(x) and x: f(x) = 15(1.25)x Which of the following graphs best represents the function? Graph of f of x equals 1.25 multiplied by 15 to the power of x Graph of exponential function going up from left to right in quadrant 1 through the point 0, 15 and continuing towards infinity Graph of f of x equals 18.75 to the power of x Graph of f of x equals 15 to the power of x

Answer 1

Answer: Graph of exponential function going up from left to right in quadrant 1 through the point 0, 15 and continuing towards infinity

Explanation:

Here the given function,

`f(x) = 15(1.25)^x`

Which is the exponential function because it is the type of
`f(x) = ab^x`,

Here, b > 1,

⇒ The graph is going up from left to right and continuing toward infinity,

Also, For x = 0,

f(x) = 15

Therefore, the y-intercept of the graph = (0,15),

That is, the function is entering in first quadrant through the point (0,15).

Thus, second Option is correct.

Note: Since, the growth factor of the given function is 1.25,

In first option function is,

`f(x) = 1.25(15)^x`

The growth factor 15 which is different from 1.25.

This is why, it is incorrect.

In third option,

`f(x)=18.75^x`

The growth factor is 18.75 which is different from 1.25.

This is why, it is incorrect.

In fourth option function is,

`f(x) = 15^x`

The growth factor is 15 which is different from 1.25,

This is why, it is incorrect.