Question

Identify the multiplier of the following exponential equation based on thetable of values belowO b= 2O b= 4O b= -4O b= 0.5

Answer 1

Given data:

The given table is shown.

The standard expression for exponential function is,

`y=a(b)^x`

Substitute -1 for x and 8 for y in the above expression.

`\begin{gathered} 8=a(b)^(-1) \\ 8=(a)/(b) \\ a=8b \end{gathered}`

Substitute 0 for x and 4 for y in the above expression.

`\begin{gathered} 4=a(b)^0 \\ a=4 \end{gathered}`

The value of b is,

`\begin{gathered} 4=8b \\ b=(1)/(2) \\ =0.5 \end{gathered}`

The expression for the exponential function is,

`y=4(0.5)^x`

Thus, the multiplier is 0.5, so last option is correct.