Question

With 300 being the y intercepts and an additional point being (3,450) How do you find a formula in the format of `ab^x`?

Answer 1

`y = 300(root(3)(3/2))^x`

Explanation:

Use the y-intercept to find `a`:

`300 = ab^0`, where `b^0=1` so `a = 300` which means `y=300b^x`

Use the point to find `b`:

`450 = 300b^3`; so `b^3 = 450/300 = 3/2 = 1.5`

this means `b = root(3)(3/2) ~~ 1.1447`

so `y = 300 (root(3)(3/2))^x = 300(root(3)(1.5))^x`