Question

Find the equation for an exponential function that passes through the pair of points given below.
Through (2, 12) and (4, 48).
f(x)=?
Use y=Ab^x; b>0
Please somebody help!

Answer 1

We know the equation is exponential. So the first step is to solve for b.

We know that there exists a point (2,12). Because the function is exponential, we know that b * 12 will give us our value when x = 3, or the point (3, b*12). If we multiply by 'b' again so b*b*12, we know it will give our value when x = 4, or the point (4, b*b*12) .... but here's the awesome thing! we have the y-value at x=4. The question tells us it is 48!

so we know that: \[ b*b*12 = 48\]
Solve for b, and you will have solved the first step of the problem! Then, sub one of the points in the question back into the equation with the new value for b, then solve for A.

With A and b, you can then determine the final equation.

Answer 2

so the answer is y=3(2^x) ?