2.4 Key features of graphsIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 2.4 Key features of graphs

1. A farmer uses 60 m of fencing to make a rectangular pen against a straight wall, so only three sides need fencing. The width of the pen, perpendicular to the wall, is $x$ metres, and its area is $A(x)=x(60-2x)$ m$^2$.
   Write down the zeros of $A$, and explain what the larger zero means in this context.2 marks
2. A school hires a coach for a trip. The cost per student, $C$ AED, is modelled by $C(n)=\frac{600}{n}+15$, where $n\ge1$ is the number of students on the trip.
   Explain what the horizontal asymptote means in this context.2 marks
3. Two colonies of bacteria are grown in a laboratory. For $0\le t\le12$ days, the number of bacteria in colony A is $P(t)=500\times1.3^t$ and the number in colony B is $Q(t)=2000+300t$. Use your GDC where appropriate.
   (i) Write down the number of bacteria in each colony at $t=0$. (ii) Find the value of $t$, for $t>0$, at which the two colonies have the same number of bacteria.3 marks