A shopkeeper earns Rs. 380 in the first week, Rs. 660 in the second week and Rs. 860 in the third week. Earning is the quadratic function of number of week for which the earning is found. a. Find the quadratic function that fits the data

9514 1404 393

  e(w) = -40w^2 +400w +20

Step-by-step explanation:

A graphing calculator or spreadsheet can do the quadratic regression and help you find the formula. Here earnings (e) as a function of weeks (w) can be expressed by ...

  e(w) = -40w^2 +400w +20

__

Further development

There are a couple of other ways you can go at this. One is to write equations for a, b, c using the standard form quadratic.

  aw^2 +bw +c = e

  a +b +c = 380 . . . . . . for week 1

  4a +2b +c = 660 . . . for week 2

  9a +3b +c = 860 . . . for week 3

The solution of this system of equations will give the coefficients of the quadratic. Your graphing calculator or any of several web sites can solve these equations for you.

__

Consider the differences between quadratic values for w = 1, 2, 3.

  e2 -e1 = (4a +2b +c) -(a +b +c) = 3a +b

  e3 -e2 = (9a +3b +c) -(4a +2b +c) = 5a +b

Then the second differences are ...

  (e3 -e2) -(e2 -e1) = (5a +b) -(3a +b) = 2a

In the given set of numbers, the first differences are ...

  660 -380 = 280 . . . . . . . call this d1

  860 -660 = 200

And the second difference is ...

  200 -280 = -80 . . . . . . . call this d2

From the above, we know that 2a = -80  ⇒  a = -40

and 3a +b = 280 = 3(-40) +b  ⇒  b = 400

Finally, a+b+c = 380 = -40 +400 +c  ⇒  c = 20

Then the generic solution is ...

  a = d2/2

  b = d1 -3a

  c = e1 -a -b . . . . . where e1 is the first-week's earnings

hello from mrbilldoesmath!

answer:

the domain is the set { -2, 0, 2, 3}

discussion:

the domain is the set of x values in the ordered pairs (x,y). taking the x, or first component, of each ordered pair gives   -2, 0, 2, 3.

you,

mrb

all group life insurance is term insurance. actually it is annual renewable term and it is rated on the average age and claims experience of the entire group, which is called "experience rating." remember, this type of insurance has a 31-day grace period and is convertible to whole life upon leaving employment. a contributory group plan requires that both the employer and the employees pay part of the premium. at least 75% of those eligible must participate, so the group is sure to get most of the healthy employees as well as those that are sick.

step-by-step explanation: