The most expensive rates in dollars per minute for a 2minute

The most expensive rates (in dollars per minute) for a 2-minute telephone call using a long-distance carrier are listed in the table. (a) Find the function for the quadratic model that gives the most expensive rates in dollars per minute for a 2-minute telephone call using a long-distance carrier, where x is the number of years since 1980, with data from 2 lessthanorequalto x lessthanorequalto 20. (Round all numerical values to three decimal places.) p(x) = dollars per minute (b) Calculate the average of the most expensive rates from 1982 through 2000. exist per minute (c) Calculate the average rate of change of the most expensive rates from 1982 through 2000. exist per minute per year

Solution

standard quadratic model is given by

y = ax^2 + bx + c

taking 3 points to find the quadratic model

first point ( 2 , 1.34 )

2nd point ( 4 , 1.22)

3rd point ( 5, 1.15)

plugging the values in standard equation and finding 3 equations

1.34 = 4a + 2b + c -------------------- eqn 1

1.22 = 16a + 4b + c -------------------- eqn 2

1.15 = 25a + 5b + c ------------------- eqn 3

solving the equation for a,b,c

a = 0.003333

b = -.127

c = 1.611

hence quadratic model is

y = 0.003333x^2 -.127x +1.611

b) average of most expensive rates are

8.19/ 18 = $ 0.455

c) average rate of change = f(2000) - f(1982) / 2000 - 1982

= .18 - 1.34 / 18

= $ 0.064