IB Math Studies – Chapter 16 and 17 – Exponential Functions – Review Questions

1.The diagrams below are sketches of some of the following functions.

(i)y = ax(ii)y = x2 – a (iii)y = a – x2

(iv)y = a – x(v)y = x – a

Complete the table to match each sketch to the correct function.

Sketch Function

(a) (b) (c) (d) Working: (Total 8 marks)

2.The following diagrams show the graphs of five functions.

Each of the following sets represents the range of one of the functions of the graphs.

(a){y y } (b){y y 2}

(c){y y > 0} (d){y 1 ≤ y ≤ 2}

Write down which diagram is linked to each set.

Working: Answers:

(a)…………………………………………..

(b)…………………………………………..

(c)…………………………………………..

(d)…………………………………………..

(Total 4 marks)

3.In an experiment researchers found that a specific culture of bacteria increases in number according to the formula

N = 150 × 2t, where N is the number of bacteria present and t is the number of hours since the experiment began.

Use this formula to calculate

(a)the number of bacteria present at the start of the experiment; (b)the number of bacteria present after 3 hours;

(c)the number of hours it would take for the number of bacteria to reach 19 200.

Working: Answers:

(a)…………………………………………..

(b)…………………………………………..

(c)…………………………………………..

(Total 4 marks)

4.In an experiment it is found that a culture of bacteria triples in number every four hours.

There are 200 bacteria at the start of the experiment.

Hours 0 4 8 12 16

No. of bacteria 200 600 a 5400 16200

(a)Find the value of a.

(1)

(b)Calculate how many bacteria there will be after one day.

(2)

(c)Find how long it will take for there to be two million bacteria.

(3)

(Total 6 marks)

5.The area, A m2, of a fast growing plant is measured at noon (12:00) each day. On 7 July the area was 100 m2. Every day the plant grew by 7.5%. The formula for A is given by

A = 100 (1.075)t where t is the number of days after 7