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:
[tex]f(x) = -1*(2)^x[/tex]
If you want to learn more about exponential functions:
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