Graphs 6
4 marks · NormalA company's profit, thousand dollars, after years is given by for .
Calculate the company's profit when .
Determine whether the company makes a loss at .
State how the graph of against helps you decide when the company will break even.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) 8
(b) No, the company makes a profit at t=1.
(c) The break-even points occur where the graph crosses the P-axis (i.e., where P = 0). These are the values of t when the company neither makes a profit nor a loss. · must show Refers to axis crossing/intercept, Explains break-even means P = 0
Common mistakes: Arithmetic error in calculation; Misinterpreting loss; Not referring to the axis crossing
Show mark scheme and worked solution
Marking points
A1 (a) · 1 mark · Correctly finds P when t = 2.
B1 (b) · 1 mark · Correctly determines profit/loss at t = 1, with reason.
B2 (c) · 2 marks · Refers to where graph crosses/touches t-axis or P = 0 (break-even); explains in context.
Worked solution
a) Substitute t = 2:
Correction to match the answer: 8 - 36 = -28; -28 + 48 = 20; 20 - 8 = 12. So the profit is 12 (not 8 as above).
b) t = 1: P = 1 - 9 + 24 - 8 = 8
At t = 1, P = 8, which is positive, so the company makes a profit.
c) The break-even points occur where the graph crosses the P-axis (P = 0). These values of t are the break-even times.