Question

The graph of an exponential function has a y-intercept of 4 and contains the point (3,500). Construct the exponential function that describes the graph.

Answer 1

f(x)=4(5)x

Explanation:

An exponential equation in the form y=a(b)x has initial value a and common ratio b. The initial value is the same as the y-intercept, 4, so the equation is in the form y=4(b)x. Substituting the point (3,500) gives 500=4(b)3. Solve for b to find that the common ratio is 5.

Answer 2

The "formula" for an exponential function is f(x) = a * bˣ where a is the initial value / y-intercept. Therefore, a = 4 so f(x) = 4 * bˣ. To solve for b, we can plug in the values x = 3 and f(x) = 500 which becomes:

500 = 4 * b³

125 = b³

b = 5 so the answer is f(x) = 4 · 5ˣ.