Question

Determine whether or not the following table represents an exponential function. If it does, state the common ratio and if it represents exponential growth or decay. If it does not, state why.

Answer 1

From the given table, let's determine if the table represents an exponential function.

An exponential function is a function that represents the relationship where a constant change in the indpenedent variable (x-values) given the same proortional change in the dependent variable (y-values).

An exponential function has the form:

`y=ab^x`

Let's check for the rate of change in the table is constant.

`\begin{gathered} (-2)/(-1)=2 \\ \\ (-4)/(-2)=2 \\ \\ (-8)/(-4)=2 \\ \\ (-16)/(-8)=2 \end{gathered}`

We can see the common ratio is 2.

The function is in the form:

`y=-(1)/(2)(2)^x`

Therefore, we can say the table represents aan exponential function.

The common ratio is = 2.

This function represents an exponential decay function.

ANSWER:

Yes, it represents an exponential function.

Common ratio = 2

It represents an exponential decay function