Question

Select the equation that represents the graph of the exponential function below.

Answer 1

Given

The graph,

The points on the graph through which the curves passes is (0,4) and (1,8).

To find the equation that represents the graph of the exponential function.

Step-by-step explanation:

It is given that,

The points on the graph through which the curves passes is (0,4) and (1,8).

Now, consider the function,

`y=4((1)/(2))^x`

Since the curve passes through (0,4) and (1,8).

Then,

`\begin{gathered} For\text{ }x=0, \\ y=4((1)/(2))^0\left[\because a^0=1\right] \\ =4*1 \\ =4 \end{gathered}`

Also,

`\begin{gathered} For\text{ }x=1, \\ y=4((1)/(2))^1 \\ =4*(1)/(2) \\ =2 \end{gathered}`

Which is not possible as the curve passes through (1,8).

Hence, a) is not the required function.

Now, consider the function,

`y=4(2)^x`

Then, for x=0,

`\begin{gathered} y=4(2)^0 \\ y=4*1 \\ y=4 \end{gathered}`

Also, for x=1,

`\begin{gathered} y=4(2)^1 \\ y=4*2 \\ y=8 \end{gathered}`

It satisfies the given conditions, that is, the curve passes through (0,4) and (1,8).

Hence, c) represents the graph of the exponential function.