Question

What is the equation for this problem?

Find a possible exponential function in y=a(b)^x form that represents each situation described below. Your answer should look like y=a(b)^x
Passes through the points (0,4) and (2,1)

Answer 1

Given: `y = a(b)^x`

Evaluate at the point `(0,4)`:

`4 = a(b)^0`

We know that `b^0 = 1`:

`4 = a(1)`

`a = 4`

The equation becomes:

`y = 4(b)^x`

Evaluate at the point `(2,1)`

`1 = 4(b)^2`

`b^2 = 1/4`

`b = +-1/2`

I assume that they want you to choose the positive value:

`y = 4(1/2)^x`

But this is not strictly correct.

`y = 4(-1/2)^x`

Is, also, a possible solution and we cannot tell which is correct without more information.