Question

How do you find the formula of an exponential graph given A = (1, 12) and B = (2, 48)?

Answer 1

This graph has a formula: `y=3*(4^x)`

Explanation:

We are looking for a function `y=a*b^x` which passes through `(1,12)` and `(2,24)`

If we substitute the points' coordinates to the function formula we get:

`{(a*b=12),(a*b^2=48):}`

If we substitute first equation to the second we get: `12*b=48`

so `b=4`

Now if we substitute `b=4` into first equation we get: `4a=12`

`a=3`

Finally we can writhe the answer: The function is: `y=3*4^x`