Cambridge International Mathematics

EXERCISE 28E

1 Show that an exponential model is appropriate for the following data, and state the equation of the

exponential model.

a x 2 5 10 20

P 44 100 401 6448

b t 1 3 6 8 11

N 4 : 6 3 : 1 1 : 7 1 : 1 0 : 6

Year 2000 2002 2005 2008

Value(E) 216 000 226 000 242 000 260 000

2

a

b Estimate the value of their house in the years

i 2004 ii 2009.

c Which of the values inbis more reliable? Give reasons for your answer.

3 The table below shows the concentration of chemicalXin the blood of an accident victim at various

times after an injection was administered.

Time (tminutes) 1 2 3 4 5 6 7

Concentration ofX(Cmicrograms/cm^3 ) 104 : 6 36 : 5 12 : 7 4 : 43 1 : 55 0 : 539 0 : 188

a Show that an exponential model fits the data well, and find the model.

b The victim is considered safe to move when the concentration ofX falls below 2 £ 10 ¡^4

micrograms/cm^3. Estimate how long it will take to reach this level.

Review set 28A

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1 Write the following in exponent form:

a

p

5 b

1

p 37 c

p (^451) d 1
p (^547)
2 Evaluate without using a calculator:
a 16
(^34)
b 125
(^23)
c 9 ¡
(^32)
d 32 ¡
(^35)
3 Let f(x)=5x.
a Find: i f(¡x) ii ¡f(x) iii 2 £f(x) iv f(2x)
b Sketch all five graphs on the same set of axes.
4 If f(x)=3x¡ 1 , find the value of:
a f(0) b f(3) c f(¡1) d f(¡2)
5 On the same set of axes, without using technology, draw the graphs of y=2x and y=2x+2:
a State they-intercepts and the equations of the horizontal asymptotes.
b What transformation is needed to draw the graph of y=2x+2from the graph of y=2x?
6 Solve forx:
a 3 x= 811 b 2 x¡^2 =^18 c 254 ¡x=1
d 4 £ 5 x= 100 e 5 £(^12 )x+1=80 f 4 x+1£ 8 x=^14
Over the last years, Jane and Pierre
have had their house valued four times.
The valuations were:

8

Does an exponential model fit this data? If so, what is the model? (Let year 2000 be t=0.)

Exponential functions and equations (Chapter 28) 577

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Y:\HAESE\IGCSE01\IG01_28\577IGCSE01_28.CDR Monday, 27 October 2008 2:44:09 PM PETER