I’m not sure how to do this problem. I have to find the exponential equation.

Accepted Solution

The general formula for an exponential equation is ab^x
Plug in (2,5) and (4,180) and solve for "a" and "b".

For (2,5) we get:

ab^2 = 5

And for (4,180) we get:

ab^4 = 180
Well, ab^4 can be rewritten as (ab^2)*b^2.

We know that ab^2 = 5, so we can substitute it into the expression above:

5*b^2 = 180
b^2 = 36
b = 6

We figured out what "b" is.  Now to figure out "a", let's use (2,5) again in our general equation again:

ab^2 = 5

But since we know what "b" is now, plug it in to solve for "a":

a(6)^2 = 5
36a = 5
a = 5/36

Thus our exponential equation is:


To figure out the other points, use the above equation and substitute the x-values.

For example, for x = -1, we have:

(5/36)*6^-1 = (5/36)/6 = 5/216