A company offers three varieties of pens: Pinnacle, Quillmaster, and RapidWrite. The cost of a Pinna

Question

A company offers three varieties of pens: Pinnacle, Quillmaster, and RapidWrite. The cost of a Pinnacle pen is $0.30$ lower than the cost of $10$ RapidWrite pens. A combination of $5$ Pinnacle pens, $4$ Quillmaster pens, and $3$ RapidWrite pens costs $29.25$. Additionally, the cost of $13$ Quillmaster pens is the same as the cost of a Pinnacle pen. By writing down three linear equations, determine the cost of a pen for each variety.[4] The company sells value packs, each consisting of a Pinnacle pen, a Quillmaster pen and a RapidWrite pen. Determine the cost of a value pack if it is sold at a discount of $20$%.[1] The sales director believes that the connection between the sales revenue, $S$ thousand dollars, and the time, $t$ years, can be modelled by $$S=3+0.2\ln(3t+1) \text{ for}\hspace{0.5em} 0\le t\le 6.$$ Sketch the graph of $S$ against $t$.[2] Find $\frac{\mathrm{d}S}{\mathrm{d}t}$ and explain in context what the expression for $\frac{\mathrm{d}S}{\mathrm{d}t}$ indicates about sales revenue for the first $6$ years.[3] Using your calculator, find the value of $\displaystyle\int\nolimits_0^4 3+0.2\ln(3t+1) \, \mathrm{d}t$. In the context of the question, what does this value represent?[2]

Accepted Answer

(a)Pinnacle = $5.20, Quillmaster =$0.40, RapidWrite =$ 0.55 (b)$4.92 (d)$\frac{dS}{\mathrm{d}t}=\frac{3}{5(3t+1)}$ (e)13.4

2024 YIJC H1 Q5

2024 YIJC H1 Q5