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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.

User Anri
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1 Answer

6 votes

Answer:


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

User Fhilton
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