Question

(1,-2) and (2,-4) exponential formula f(x)=ab^x

Answer 1

We conclude that the exponential function is:

f(x) = -1*(2)ˣ

How to find the exponential function?

Here we know that we have an exponential function of the form:

$f(x) = a*b^x$

And we know two points on the function, that are:

$f(1) = -2 = a*b^1 = a*b\\\\f(2) = -4 = a*b^2$

Then we have a system of equations to solve, which is:

$-2 = a*b\\-4 = a*b^2$

From the first equation we can solve:

$-2/a = b$

Replacing that in the other equation we can get:

$-4 = a*(-2/a)^2 = 4/a\\\\a = 4/-4 = -1$

Now that we know the value of a, we can get the value of b:

$-2/a = b\\\\-2/-1 = 2 = b$

In this way, we conclude that the exponential function is:

$f(x) = -1*(2)^x$

If you want to learn more about exponential functions:

brainly.com/question/11464095

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