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:

$y = 13.72 \times (1.4)^x$

Step-by-step 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'

$5=a.(1.4)^{-3}$

$a=\frac{5}{(1.4)^{-3}} =5 \times (1.4)^3= 5 \times 2.744$

$a = 13.72$

So the exponential model of best fit is,

$y = 13.72 \times (1.4)^x$