42 EBook Readers The table lists the projected number of shi

42. E-Book Readers The table lists the projected number of shipments S of e-book readers in millions, x years after 20 1 1 . YearS 23 15 3 (a) Evaluate S(3) and interpret the result.

Solution

Solution:

a)

let the function be;

f(x) = ax² + bx + c

=> 23 = c (putting f(x) as 23 and x as 0 from the table it self)

=> 15 = a + b + 23 (putting f(x) as 15 and x as 1 from the table it self)-----Equation-1

=> 11 = 4a + 2b + 23 (putting f(x) as 11 and x as 2 from the table it self)-----Equation-2

On solving these two equation;

we get;

a =9.5 and b = -17.5

hence;

f(x)= 9.5x² - 17.5x +23

b)

we have to calculate the value of x for given value of f(x)

=> 2017 = 9.5x² - 17.5x +23

=> 9.5x² - 17.5x -1994 = 0

=> x = no. of shipments = 15.44 (i.e, 15 because it must be an integer value)