Question

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

Answer 1

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:

$y=(-8)2^x$