Mathematical Methods — Question 9

QCAA 2021, Paper 2 · 1 mark

Q9 · 2021 · Technology-activeSimple familiar1 mark

QUESTION 9

The graphs of the functions

f(x)=2e^x+5

and

g(x)=\dfrac3{e^x}

intersect at point A. Determine the coordinates of point A.

(A)

(1.609,15)

(B)

(1.099,1)

(C)

(0.4065,2)

(D)

(-0.693,6)

ABCD

WORKED SOLUTION

1 mark

ANSWER

Worked solution

Set

2e^x+5=3e^{-x}

. With

y=e^x>0

2y^2+5y-3=0

, so

y=1/2

. Hence

x=\ln(1/2)\approx-0.693

and

y

-coordinate

=2(1/2)+5=6

Selects option D.

[1 mark]

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