Question

I'm not sure how to solve this got it off of Khan Academy.
The exponential function hhh, represented in the table, can be written as h(x)=a\cdot b^xh(x)=a⋅b
x
h, left parenthesis, x, right parenthesis, equals, a, dot, b, start superscript, x, end superscript.
xxx h(x)h(x)h, left parenthesis, x, right parenthesis
000 777
111 999
Complete the equation for h(x)h(x)h, left parenthesis, x, right parenthesis.

Answer 1

well, looking at the table there, we can see that when x = 0, h(x) = 7, and when x = 1, h(x) = 9, so let's start

$h(x)=a\cdot b^x \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=0\\ h(x)=7 \end{cases}\implies 7=a\cdot b^0\implies 7=a\cdot 1\implies 7=a~\hfill \underline{h(x)=7b^x} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=1\\ h(x)=9 \end{cases}\implies 9=7b^1\implies 9=7b\implies \cfrac{9}{7}=b~\hfill \underline{h(x)=7\left( \frac{9}{7} \right)^x}$