Question

Use the point (4,16) to substitute values into the equation f(x)=a^(x). Solve the resulting equation for a. Then give an equation of the form f(x)=a^(x) to define the exponential function.

Answer 1

The given point on the function is (4,16); in other words, when x equals 4, f(x) equals 16. Let's substitute these values into the formula:

16 = a^(4)

To solve for a, we have to isolate a on one side of the equation. To do this, we can take the fourth root of both sides of the equation. When we take the fourth root of 16, we get 2.

So, a = 2.

Now that we have the value of a, our exponential function can be written as:

f(x) = 2^(x).