Cambridge International Mathematics

Example 8 Self Tutor

The currentIflowing through the electric circuit in a fan,tmilliseconds after it is switched off, is

given by I= 320£ 2 ¡^0 :^5 tmilliamps.

a Find the initial current in the circuit.

b Find the current after: i 4 ii 10 milliseconds.

c GraphIagainstt.

d Use technology to find how long it takes for the current to drop to 50 milliamps.

a When t=0, I= 320£ 2 ¡^0 :^5 £^0

= 320milliamps

biWhen t=4,

I= 320£ 2 ¡^0 :^5 £^4

= 320£ 2 ¡^2

= 320£^14

=80milliamps

ii When t=10,

I= 320£ 2 ¡^0 :^5 £^10

= 320£ 2 ¡^5

= 320£ 321

=10milliamps

cdWe plot Y 1 = 320£ 2 ¡^0 :^5 X and Y 2 =50

on the same axes.

The graphs meet when X¼ 5 : 36

) it takes approximately 5 : 36 milliseconds

for the current to drop to 50 milliamps.

EXERCISE 28D

1 A local zoo starts a breeding program to ensure the survival of a species of mongoose. From a previous

program, the expected population innyears’ time is given by P=40£ 20 :^2 n.

a What is the initial population purchased by the zoo?

b What is the expected population after:

i 3 years ii 10 years iii 30 years?

c GraphPagainstn.

d How long will it take for the population to reach 100?

2 In Tasmania a reserve is set aside for the breeding of echidnas. The

expected population size aftertyears is given by P=50£ 2

t 3

:

a What is the initial breeding colony size?

b Find the expected colony size after:

i 3 years ii 9 years iii 20 years.

c GraphPagainstt.

d

5 10 15

300

200

100

I(mA)

t(milliseconds)

320

I¡=¡50

» 5. 36

I= 320 ́ 2 -^0.^5 t

O

How long will it take for the echidna population to reach 150?

574 Exponential functions and equations (Chapter 28)

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