Question

Write an equation for the exponential function represented in the graph below.

Answer 1

Answer: y=4(2)ˣ or y=4 · 2ˣ or f(x)=4(2)ˣ or f(x)=4 · 2ˣ

Explanation:

Saw this on Algebra Nation, got it correct.

Answer 2

`y=4(2^x)`

Explanation:

we know that

The exponential function is of the form

`y=a(b^x)`

where

a is the initial value or y-intercept

b is the base or factor growth

r is the rate of change

In this problem we have

looking at the graph

Is a exponential growth function (as the value of x increases the value of y increases)

so

`b > 1`

The y-intercept is the point (0,4)

so

`a=4`

substitute

`y=4(b^x)`

From the graph take the point (1,8)

substitute in the exponential function and solve for b

`8=4(b^1)\\b=8/4\\b=2`

therefore

The exponential function is equal to

`y=4(2^x)`