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weqwewe [10]
3 years ago
8

The graph of an exponential function passes through (2,−32) and (3,−64). Find the exponential function that describes the graph.

Mathematics
1 answer:
Greeley [361]3 years ago
7 0

Answer: y=(-8)2^x

Step-by-step explanation:

The exponential function will have this form:

y=ab^x

We know that the function passes through the points (2,-32) and (3,-64). Then, we can substitute the coordinates of the point (2,-32)  into y=ab^x and solve for "a":

-32=ab^2\\\\a=\frac{-32}{b^2}

Then, we know that:

y=(\frac{-32}{b^2})b^x

Now, we neeed to substitute the coordinates of the second point (3,-64) into y=(\frac{-32}{b^2})b^x and solve for "b":

-64=(\frac{-32}{b^2})b^3\\\\-64=-32b\\\\\frac{-64}{-32}=b\\\\b=2

Substituting the value of "b" into a=\frac{-32}{b^2} we can find "a":

a\frac{-32}{2^2}\\\\a=-8

Therefore, we get that the exponential function that describes the graph, is:

y=(-8)2^x

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