This graph shows an exponential function.
(1, -12) (2, -48)
Write an equation for the function in the form f(x)=a(b)x.
f(x)=
f(x) = a(b)^x
Given that (1, -12) is a point on the graph, we can substitute the values of x and f(x) into the equation:
-12 = a(b)^1
Simplifying:
-12 = ab
Similarly, substituting the values of (2, -48):
-48 = a(b)^2
Simplifying:
-48 = ab^2
From the two equations, we can solve for a and b. Dividing the second equation by the first equation:
(-48)/(-12) = (ab^2)/(ab)
4 = b
Substituting the value of b into the first equation:
-12 = a(4)^1
-12 = 4a
Dividing both sides by 4:
-3 = a
Thus, the equation for the exponential function is:
f(x) = -3(4)^x