Question

1. Find the exponential model of best fit for the points (−3,5),(1,12),(5,72),(7,137). Explain how you got your answer. Round values to the nearest hundredth.

Answer 1

`y = 13.72 * (1.4)^x`

Explanation:

The general exponential equation is written as,

`y=a.b^x`

We can consider two of the points to find the values of 'a' and 'b'. Let us consider the points (-3, 5) and (5, 72)

Putting (-3, 5) in the general equation we get,

`5=a.b^(-3)` .................. (i)

Putting (5, 72) in the general equation we get,

`72=a.b^(5)` ...................(ii)

Dividing equation (ii) by (i) we get,

`14.4 = b^(5-(-3))=b^8`

Solving for 'b', we get,

`b=1.4`

Putting the value of 'b' in equation (i) we can find the value of 'a'

`5=a.(1.4)^(-3)`

`a=(5)/((1.4)^(-3)) =5 * (1.4)^3= 5 * 2.744`

`a = 13.72`

So the exponential model of best fit is,

`y = 13.72 * (1.4)^x`