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

Step1: Identify y-intercept (a)

The graph crosses the y-axis at $(0,1)$. For $y=a(b)^x$, when $x=0$, $y=a(b)^0=a$. So $a=1$.

Step2: Find growth factor (b)

Pick another point on the graph, e.g., $(1,2)$. Substitute $x=1$, $y=2$, $a=1$ into the function:
$2=1(b)^1$
Solve for $b$: $b=2$.

Step3: Write the function

Substitute $a=1$ and $b=2$ into $y=a(b)^x$.

Answer:

$y=1(2)^x$ or simplified as $y=2^x$