Cambridge International Mathematics

EXERCISE 28C.2

1 Solve forx, giving answers correct to 3 decimal places:

a 2 x= 100 b 2 x=0: 271 c 2 x=¡ 3

d 5 x=8 e 7 ¡x=23 f 9 x= 10 000

g 3 x=0:006 51 h 5 £ 2 ¡x=18 i 200 £ 2 x= 5800

j 300 £ 2 ¡^3 x=4: 1 k 25 £ 3 ¡^2 x=0: 035 l 4 £ 2 ¡^0 :^02 x=0: 07

m 3 x+1=4 n 23 x¡^2 =5 o 3(2x¡^2 )=1

Exponential functions model real life situations in many branches of science and commerce. Common

applications include compound interest and biological modelling.

Example 7 Self Tutor

During a locust plague, the area of land eaten is given by A= 8000£ 20 :^5 n hectares wherenis

the number of weeks after the initial observation.

a Find the size of the area initially eaten.

b Find the size of the area eaten after: i 4 weeks ii 7 weeks.

c GraphAagainstn.

d How long would it take for the area eaten to reach50 000hectares?

a Initially, n=0 ) A= 8000£ 20

) A= 8000hectares

biWhen n=4,

A= 8000£ 20 :^5 £^4

= 8000£ 22

= 32 000ha

ii When n=7,

A= 8000£ 20 :^5 £^7

= 8000£ 23 :^5

¼90 500ha

cdWe plot Y 1 = 8000£ 20 :^5 X and

Y 2 = 50 000 on the same axes.

The graphs meet when X¼ 5 : 29

) it takes approximately 5 : 29 weeks for

the area eaten to reach50 000hectares.

PROBLEM SOLVING WITH EXPONENTIAL

FUNCTIONS [3.2]

D

2 4 6

100000

80000

60000

40000

20000

nweeks

A(ha)

8000

O

A¡=¡50¡000

A= 8000 ́ 20.^5 n

» 5. 29

Exponential functions and equations (Chapter 28) 573

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