How would you find the values of a and b in the equations y=ab^x if you know the values of x and y?

Question

I would like to get the help as soon as possible. Thanks

Answer 1

You actually need two (x,y) points to figure out the equation. Suppose you are given the points (1,6) and (3,54). Here are the steps.

1) Plug in both points:

y = ab^x

6 = ab¹

54 = ab³

2) To find the value of b, take the ratio of the two:

54/6 = ab³/ab¹

9 = b²

3 = b

So your equation so far is y = a·3^x

3) To find the value of a, plug in one of the two points and solve for a:

y = a·3^x

Plug in (1,6)

6 = a·3¹

2 = a

The final equation is y = 2·3^x