Question

Find the equation of the exponential function represented by the table below

Answer 1

`y=4(4)^x`

Explanation:

Exponential functions are represented in the form
`y=a(b)^x`, where a is the initial value and b is the multiplier.

Here, we see that when x = 0, y = 4. This means that 4 is our initial value, or a. You can look at the a variable almost being like the y-intercept of a graph.

Next, we must solve for b. We can do 16 ÷ 4 to find the slope, or multiplier of this function, because 16 is 1 input x-value up from 0. 16 ÷ 4 = 4.

So, we now have all the needed variables, so we plug them into the formula

`y=a(b)^x`