Note: This is the Solution of review exercise 10.2 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward.
Exercise 10.2
Question # 01: Plot the graph of \(\small{y=2x^2-4x+3}\) from \(\small{-1}\) to \(\small{3}\). Draw tangent at \(\small{(2,3)}\) and find the gradient.
Question # 02: Plot the graph of \(\small{y=3x^2+x+1}\) and draw tangent at \(\small{(1,5)}\). Also find gradient of the tangent line at this point.
Question # 03: The strength of students in a school was \(\small{1000}\) in \(\small{2016}\). If the strength decay according to the equation \(\small{S=1000e^{-t}}\), where \(\small{S}\) is the number of students at time \(\small{t}\).
\( (a) \; \) Graph the given equation for \(t=0\) in \(2016\) to \(t=9\) in \(2025\).
\( (b) \; \) From the graph, estimate the student’s strength in \(2019\) and in \(2023\)
Question 4: The demand and supply functions for a product are given by the equations \(\small{P_{d}=400-5Q}\), \(\small{P_{s}=3Q+24}\):
Plot the graph of each function over the interval \(\small{Q=0}\) to \(\small{Q=300}\).
Question 5: Shahid’s salary \(\small{S(x)}\) in rupees is based on the following formula:
\(\small{S(x)=45000+4500x}\)
where \(\small{x}\) is the number of years he has been with the company. sketch and interpret the graph of salary function for \(\small{0 \le x \le 5}\).
Question 6: A company manufacturers school bags. The cost function of producing \(\small{x}\) bags is \(\small{C(x)=1200+800x}\) and the revenue from selling \(\small{x}\) bags is \(\small{R(x)=25x}\).
\( (a) \; \) Find the break-even point.
\( (b) \; \) Determine the profit or loss when \(250\) bags are sold.
\( (c) \; \) Plot the graphs of both the functions and identify the break-even point.