Find the equation of the exponential function represented by the table below: xx yy 00 44 11 1212 22 3636 33 108108

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Answer 1

Hi Houston,

Question: Find the equation of the exponential function represented by the table

( x ,y) (0, 4) (1, 12) (2, 36) (3, 108)

Given:

1. Exponential Equation
2. Table of Values

The exponential Equation means that we can use the form

y=a b^x Where a is the initial value and b is the constant ratio

You can use the data points given to solve for both a and b

Use data point (0,4) to solve for a

y=a b^x

4=a b⁰

4 = a

You can use another data point to solve for b

Data point (1,12) and the value of a from above (a=4)

y=a b^x

12=4 (b¹)

3 = b

Now you have both values and can write your equation.

y=a b^x

y=4(3^x)

Lets check the other data points given to see if the equation works

(2, 36)

y=4(3²)

y = 36 This works

(3, 108)

y=4(3³)

y=108

This also works.

Hope this helps!