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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)

User Rolice
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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).

User Adi Tiwari
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8.3k points

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