Mathematical Methods — Question 2

QCAA 2021, Paper 2 · 1 mark

Q2 · 2021 · Technology-activeSimple familiar1 mark

QUESTION 2

A substance is being heated such that its temperature

T

^\circ

C after

t

minutes is given by the function

T=2e^{0.5t}

. The first integer value of

t

for which the instantaneous rate of change of temperature is greater than

100\ ^\circ

C per minute is

(A)

t=10

(B)

t=9

(C)

t=8

(D)

t=7

ABCD

WORKED SOLUTION

1 mark

ANSWER

Worked solution

T'(t)=e^{0.5t}

. Requiring

e^{0.5t}>100

gives

t>2\ln100\approx9.21

, so the first integer is 10.

Selects option A.

[1 mark]

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