Question 1

Paper 1Medium6 marks

During an 8-hour monitoring period, the water depths in two tanks are modelled by

f(t)=−0.25(t−4)2+10,g(t)=t+2,f(t)=-0.25(t-4)^2+10,\qquad g(t)=t+2,

where f(t)f(t) is the depth in Tank A, g(t)g(t) is the depth in Tank B, and tt is the time in hours since monitoring began. Depths are in centimetres, and 0≤t≤80\leq t\leq 8

(a)

Construct a function D(t)D(t) such that D(t)>0D(t)>0 means Tank A is deeper than Tank B. Give D(t)D(t) in expanded form.

[2]
(b)

Use a GDC to graph y=D(t)y=D(t) then sketch the graph for 0≤t≤80\leq t\leq 8 in your answer booklet. Label both axes with units and indicate the yy-intercept, turning point, tt-intercept and value at t=8t=8

[3]
(c)

Use your sketch to state which tank has the greater depth at t=7t=7

[1]

More AI 2.1 Functions and graphs questions