User interface language: English | Español

Date May 2018 Marks available 3 Reference code 18M.1.sl.TZ2.10
Level SL only Paper 1 Time zone TZ2
Command term Find Question number 10 Adapted from N/A

Question

The following function models the growth of a bacteria population in an experiment,

P(t) = A × 2t,  t ≥ 0

where A is a constant and t is the time, in hours, since the experiment began.

Four hours after the experiment began, the bacteria population is 6400.

Find the value of A.

[2]
a.

Interpret what A represents in this context.

[1]
b.

Find the time since the experiment began for the bacteria population to be equal to 40A.

[3]
c.

Markscheme

6400 = A × 24     (M1)

Note: Award (M1) for correct substitution of 4 and 6400 in equation.

(A =) 400     (A1) (C2)

[2 marks]

a.

the initial population OR the population at the start of experiment      (A1) (C1)

[1 mark]

b.

40A = A × 2t  OR  40 × 400 = 400 × 2t       (M1)

Note: Award (M1) for correct substitution into equation. Follow through with their A from part (a).

40 = 2t     (M1)

Note: Award (M1) for simplifying.

5.32  (5.32192…) (hours)  OR  5 hours 19.3 (19.3156…) minutes     (A1) (C3)

[3 marks]

 

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 6 - Mathematical models » 6.4 » Exponential models.
Show 55 related questions

View options