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The equation is h(x) = 45(1/5)^x

This is the same as h(x) = 45(0.2)^x because 1/5 = 0.2

Explanation:

We'll start with y = a*b^x, and plug in x = 0 to find that,

y = a*b^x

y = a*b^0

y = a*1

y = a

The table says that y = 45 is the case when x = 0. So that must mean a = 45.

The value of ''a' is the y intercept and it's the initial value.

So the equation y = a*b^x updates to y = 45*b^x

Let's plug in (x,y) = (1,9) and solve for b

y = 45*b^x

9 = 45*b^1

9 = 45b

45b = 9

b = 9/45

b = 1/5

b = 0.2

Therefore, the equation in fraction form is y = 45(1/5)^x

That same equation in decimal form is y = 45(0.2)^x

To verify the equation, plug in various values of x and you should get y values that are shown in the table.

For instance, plug in x = 2 to find that

y = 45(0.2)^x

y = 45(0.2)^2

y = 45(0.04)

y = 1.8

which matches with the table. That verifies the 5th row. I'll let you verify the other rows.