Find the exponential function f ( x ) = a x that passes through the point ( 3 , 216 ) and has a y-intercept of 1.

Answer 1

216 = ax³

1 = ax⁰

1 = a

216 = x³

6 = x

y = x³

Answer 2

We can rephrase this question as finding the exponential function that passes through the points (0, 1) and (3, 216). That is, we move 3 along x and then move 216 along y. Exponential functions are generally given by a^(x) where a is some constant number. Thus we know that, with this unction, a^(0) = 1 and a^(3) = 216. To determine what a is we need to take the cubic root of 216. Working with this number a bit we can see that 216 = 6*6*6 thus the cubic root of 216 = 6. a = 6 giving us the exponential function f(x) = 6^(x) as our result.