Question

the exponential function h, whose graph is given below, can be written as h(x) = a·b^x. complete the equation for h(x). h(x) =

Explanation:

Step1: Find $a$ using $x=0$

When $x=0$, $b^0=1$, so $h(0)=a$. From the graph, $h(0)=3$. Thus, $a=3$.

Step2: Substitute $(1,6)$ to find $b$

Substitute $x=1$, $h(1)=6$, $a=3$ into $h(x)=a\cdot b^x$:
$6=3\cdot b^1$
Solve for $b$: $b=\frac{6}{3}=2$

Step3: Write the final function

Substitute $a=3$ and $b=2$ into the general form.

Answer:

$h(x)=3\cdot 2^x$