Mathematical Methods — Question 6

QCAA 2020, Paper 2 · 1 mark

Q6 · 2020 · Technology-activeSimple familiar1 mark

QUESTION 6

Oil is leaking from a tanker at the rate of

r(t)=9000e^{-0.2t}

litres per hour, where

t

is in hours. Determine how much oil leaks from the tanker (to the nearest litre) from time

t=0

to time

t=10

(A)

38 910 litres

(B)

8756 litres

(C)

7782 litres

(D)

1556 litres

ABCD

WORKED SOLUTION

1 mark

ANSWER

Worked solution

\int_0^{10}9000e^{-0.2t}dt=45000(1-e^{-2})\approx38910

litres. Hence A.

Selects option A.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.