Question

x -1 0 1 2 h(x) 4 12 36 108write an exponential function of the form y=ab^x

Answer 1

Answer:

$y=12(3)^x$

Explanation:

Given the form of the exponential function:

$y=ab^x$

In the pair: (0,12)

$\begin{gathered} x=0,y=12 \\ \implies12=a\times b^0 \\ \implies12=a\times1 \\ a=12 \end{gathered}$

Substituting a=12, and the point (1,36):

$\begin{gathered} y=ab^x \\ 36=12\times b^1 \\ 12b=36 \\ b=\frac{36}{12} \\ b=3 \end{gathered}$

Thus, the exponential function is:

$y=12(3)^x$