Question

A owner of a rapidly expanding business finds the first five months of the year the sales (in thousands dollars) are $4.0, $4.4, $5.2, $6.4 and $8.0 . The owner plots these figures on a graph and conjunctures that for the rest of the year the sales curve can be approximated by a quadratic polynomial . Find the least square quadratic polynomial fit the sale curve , and project the sales for the twelve months of the year.

Answer 1

f(x) = 0.2x² - 0.2x  + 4  fit the  sale curve

Step-by-step explanation:

Let say

f(x)  = ax²  + bx  + c

f(1) = 4

=> 4 = a + b + c

f(2) = 4.4

=> 4.4 = 4a + 2b  + c

f(3) = 5.2

=> 5.2 = 9a  + 3b + c

3a + b  = 0.4

5a + b  = 0.8

=> 2a = 0.4

=> a = 0.2

b = -0.2

a + b + c = 4

=> c = 4

=> f(x) = 0.2x² - 0.2x  + 4

Lets check for f(4) & f(5)

f(4) = 0.2 * 4² - 0.2*4  + 4  = 6.4

f(5) = 0.2 * 5² - 0.2*5  + 4  = 8

f(12) = 0.2 * 12² - 0.2*12  + 4  = 30.4 $

f(x) = 0.2x² - 0.2x  + 4  fit the  sale curve

30.4 $ sale in 12th Month

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