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

Answer:

$y=11.93\cdot (1.42)^x.$

Step-by-step explanation:

Find the exponential model of best fit for the points (−3,5), (1,12), (5,72), (7,137) as a function

$y=a\cdot b^x.$

Use the graphing calculator to plot points on the coordinate plane and connect them by a line that is the graph of the exponential function

$y=11.93\cdot (1.42)^x.$

You can find a and b substituting coordinates of the points  (−3,5) and (7,137) into the equation $y=a\cdot b^x:$

$5=a\cdot b^{-3},\\ \\137=a\cdot b^7.$

Then

$\dfrac{137}{5}=\dfrac{ab^7}{ab^{-3}}=b^{10},\\ \\b=\sqrt[10]{27,4}\approx 1.42.$

Then $a=5b^3=5\cdot (1.42)^3\approx 11.93.$