Answer: 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.
