Question

For the questions 3 and 4 I need help please if read directions in the picture.

Answer 1

Given the table:

x 0 1 2 3 4 5

y 500 550 605 655.5 732.05 805.255

Let's determine the type of function represented in the table.

First check if it's an exponential relationship.

Apply the formula:

`f(x)=ab^x`

Where:

a is the initial value (at x = 0)

b is the growth/decay factor.

From the table, we have:

a = 500

Let's determine if the rate of change is constant.

`\begin{gathered} b=(550)/(500)=1.1 \\ \\ b=(605)/(550)=1.1 \\ \\ b=(732.05)/(665.5)=1.1 \\ \\ b=(805.255)/(732.05)=1.1 \end{gathered}`

Therefore, the growth factor is 1.1

Since the growth factor is greater than 1, this is an exponential growth relationship.

The relationship is an exponential relationship.

The exponential function represented in the table is:

`y=500(1.1)^x`

ANSWER:

Exponential relationship.

`y=500(1.1)^x`