f ( x ) = a ⋅ b ^2 passing through (0, 8) and (2, 200)

Answer 1

Hello Liana,

Since the equation is f(x) = a* b^x, it can be solved by setting up 2 equations using the ordered pairs (0,8) and (2, 200).

Recall that y=f(x). That means you will replace the exponent x by the x-coordinate of the ordered pair, and you'd replace y by the corresponding y-coordinate.

For the ordered pair (0,8) you would have: 8 = a*b⁰ Let's call it E1.

If you remember the laws of exponents, b⁰ = 1, so E1 becomes: 8 = a*1, so 8 =a.

You would set up another equation for the 2nd ordered pair (2, 200): 200= a*b². Let's call it E2

You already know a, so the only unknown is b. You would just solve for b. Once you find b, your job is 99% done, and all you have to do is:

1. take the original equation f(x) = a*b^x
2. replace a and b by the values you found
3. That's it!

Cheers.