Answer:
f(x) = 12*(2)^x
Step-by-step explanation:
A generic exponential equation is written as:
f(x) = A*(r)^x
And we also know that this equation passes through:
(-1, 6)
(0, 12)
(1, 24)
(2, 48)
For the second point, (0, 12) we know that when f(0) = 12
Then:
f(0) = 12 = A*(r)^0
And for every real number different than zero, a^0 = 1
Then:
f(0) = A*1 = A = 12
Then the equation is:
f(x) = 12*(r)^x
Now we can use one of the other points, like (1, 24)
Then f(1) = 24
We can solve:
f(1) = 24 = 12*(r)^1 = 12*r
24/12 = r
2 = r
Then the equation is f(x) = 12*(2)^x
Now we need to check if this function also passes through the points (-1, 6) and (2, 24):
f(-1) = 12*(2)^-1 = 12/2 = 6
f(2) = 12*(2)^2 = 12*4 = 48
Nice.
So we can see that the function is f(x) = 12*(2)^x
