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.

$\begin{gathered} 8=a(b)^{-1} \\ 8=\frac{a}{b} \\ a=8b \end{gathered}$

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,

$\begin{gathered} 4=8b \\ b=\frac{1}{2} \\ =0.5 \end{gathered}$

The expression for the exponential function is,

$y=4(0.5)^x$

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