# Chapter 16 and 17 review questions

**Topics:**Analytic geometry, Dimension, Cartesian coordinate system

**Pages:**10 (3303 words)

**Published:**October 24, 2014

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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 July. (on 7 July, t = 0)The graph of A = 100(1.075)t is shown below.

7 July

(a)What does the graph represent when t is negative?

(2)

(b)Use the graph to find the value of t when A = 178.

(1)

(c)Calculate the area covered by the plant at noon on 28 July. (3)

(Total 6 marks)

6.The number of bacteria (y) present at any time is given by the formula: y = 15 000e–025t, where t is the time in seconds and e = 2.72 correct to 3 s.f. (a)Calculate the values of a, b and c to the nearest hundred in the table below: Time in seconds (t) 0 1 2 3 4 5 6 7 8

Amount of bacteria (y) (nearest hundred) a 11700 9100 7100 b 4300 3300 2600 c (3)

(b)On graph paper using 1 cm for each second on the horizontal axis and 1 cm for each thousand on the vertical axis, draw and label the graph representing this information. (5)

(c)Using your graph, answer the following questions:

(i)After how many seconds will there be 5000 bacteria? Give your answer correct to the nearest tenth of a second. (ii)How many bacteria will there be after 6.8 seconds? Give your answer correct to the nearest hundred bacteria. (iii)Will there be a time when there are no bacteria left? Explain your answer. (6)

(Total 14 marks)

7.Under certain conditions the number of bacteria in a particular culture doubles every 10 seconds as shown by the graph below.

(a)Complete the table below.

Time (seconds) 0 10 20 30

Number of bacteria 1

(b)Calculate the number of bacteria in the culture after 1 minute. Working: Answer:

(b).................................................................. (Total 4 marks)

8.The diagram below shows a part of the graph of y = ax. The graph crosses the y-axis at the point P. The point Q (4, 16) is on the graph. Diagram not to scale

Find

(a)the coordinates of the point P;

(b)the value of a.

Working: Answers:

(a).................................................................. (b)……………………………………..........

(Total 8 marks)

9.The figure below shows the graphs of the functions y...

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