Question

Nitin raised a fund for the national environmental day. The amount (in thousands) on any given day after the start of fundraising event is given by a quadratic function f(x) = ax2 + bx + c , where f(x) is the money in thousand and x is the given day. If the amount collected on the first 3 days is 9, 10, and 13, then find the amount raised on the 10th day.

• A. 70 thousand
• B. 80 thousand
• C. 90 thousand
• D. 100 thousand

Answer 1

Answer: (C)

90 thousand

Answer 2

From the given values, we get the following:
f(1) = a(1)2+ b(1) + c = 9........ (1)
f(2) = a(2)2+ b(2) + c = 10........ (2)
f(3) = a(3)2+ b(3) + c = 13....... (3)
Then, (2) − (1)gives 3a + b = 1......(4)
(3) − (2)gives 5a + b = 3........ (5)
(5) − (4)gives 2a = 2; thus, a = 1, b =− 2, c = 10
So, the amount on 10th day is
f(10) = (1)(10)2 − 2(10) + 10 = 100 − 20 + 10 = 90
So, the correct option is (C): 90 thousand.