1. A clay pigeon is released from a trap at B. The equation of its path is given by f (x) = 2 x , where x is in metres. At the same instant a gun is fi red from C and the shot travels along a straight line with equation g (x) = –x + 4.
y y = 2 x A
Clay pigeon f
B
Shot g
C x
(a) Use the table below to plot f and g on the same diagram. Give all answers in the table correct to one decimal place.
x f
g
(b) Use the graphs to fi nd the co-ordinates of the point A at which the shot hits the clay pigeon, correct to one decimal place.
2. Two functions f and g are defi ned for x ∈ R as follows: f : x → x 3 – 4x 2 + x + 6 g : x → 3
_ 2 ( 2 x )
(a) Complete the table below and use it to draw the graphs of f and g for –1 ≤ x ≤ 3. x
–1 0123
f (x) g(x)
(b) Use your graphs to estimate the values of x for which x 3 − 4x 2 + x + 6 − 3 _
decimal place.
Colony 1: P1 = 75t – t 3 + 10, 0 ≤ t ≤ 7 Colony 2: P2 = 30 × (1⋅5) t, 0 ≤ t ≤ 7 where:
P1 is the population of colony 1 in thousands. P2 is the population of colony 2 in thousands.
2 ( 2 x ) = 0, correct to one 3. The populations of two colonies of insects vary with time t in days, according to the equations: 0 0⋅5 1 1·5 2 2⋅5 3
