Question

write an exponential function for the graph. write the function in the form $y = a(b)^x$.
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Explanation:

Step1: Find a using y-intercept

The y-intercept of the graph is (0,4). For $y=a(b)^x$, when $x=0$, $y=a(b)^0=a$. So $a=4$.

Step2: Find b using another point

Pick the point (1,8). Substitute $x=1$, $y=8$, $a=4$ into the function:
$8=4(b)^1$
Solve for $b$: $b=\frac{8}{4}=2$

Step3: Write the final function

Substitute $a=4$ and $b=2$ into $y=a(b)^x$.

Answer:

$y=4(2)^x$