Final answer:
To find the exponential function h(x)=a•b^x that passes through the points (-2, 32) and (2, 1/8), we solve a system of equations derived from those points to find a=2 and b=1/4. Therefore, the function is h(x) = 2•(1/4)^x.
Step-by-step explanation:
To determine the equation of the exponential function in the form h(x)=a•b^x that passes through the points (-2, 32) and (2, 1/8), we will use the given points to find the values of a and b. The steps are as follows:
Write down the system of equations using the points and the exponential function form:
32 = a•b^(-2)
1/8 = a•b^2
Next, we have to solve this system for a and b. To find b, we divide the second equation by the first equation:
(1/8) / 32 = (ab^2) / (ab^(-2))
1/256 = b^4
b = (1/256)^(1/4)
b = 1/4
Now, we substitute b back into one of the equations to find a:
32 = a(1/4)^(-2)
32 = a•(4^2)
32 = a•16
a = 2
So, our exponential function is:
h(x) = 2•(1/4)^x
This function will pass through the points (-2, 32) and (2, 1/8).