Question

What would be the answer to this problem, I can’t get the right answer.

Answer 1

The best way to answer this question would be to try out the choices that are available. Use the choices to find the value of y for each value of x.

Let's try the first one.

`y=5(2^x)+4`
`y=5(2^x)+4`

Let's solve for y when x = -2.

`\begin{gathered} y=5(2^(-2))+4 \\ y=5((1)/(2^2))+4 \\ y=5(0.25)+4 \\ y=5.25 \end{gathered}`

Because y = 5.25 and not 2.25 when we use the first equation, then that option is wrong. Let's try the second one.

`y=-5(2^x)-4`

Again, when x = -2,

`\begin{gathered} y=-5(2^(-2))-4 \\ y=-5((1)/(2^2))-4 \\ y=-5(0.25)-4 \\ y=-1.25-4 \\ y=-5.25 \end{gathered}`

The answer is -5.25, which means this option is also wrong. Let's try the third one.

`y=-5(2^x)+4`
`\begin{gathered} y=-5(2^(-2))+4 \\ y=-5((1)/(2^2))+4 \\ y=-5(0.25)+4 \\ y=-1.25+4 \\ y=2.75 \end{gathered}`

Because the y-value is 2.75, we can try out the other values of x to make sure that it is also correct when the values of x are changed.

For x = -1:

`\begin{gathered} y=-5(2^(-1))+4 \\ y=-5((1)/(2))+4 \\ y=-5(0.5)+4 \\ y=-2.5+4 \\ y=1.5 \end{gathered}`

For x = 0:

`\begin{gathered} y=-5(2^0)+4 \\ y=-5(1)+4 \\ y=-5+4 \\ y=-1 \end{gathered}`

Foor x = 1:

`\begin{gathered} y=-5(2^1)+4 \\ y=-5(2)+4 \\ y=-10+4 \\ y=-6 \end{gathered}`

We see that for almost all of the values of x, the y-values are the same as those given in the table. Since we have tried 4 points already, it is safe to assume that the third option is the correct answer.

The answer is y = -5(2^x)+4.