Cambridge International Mathematics

3 In Uganda, the number of breeding females of an endangered population of gorillas isG 0. Biologists

predict that the number of breeding femalesGinnyears’ time will, if left alone by man, grow according

to G=G 0 £ 50 :^07 n.

a If initially 28 breeding females are in the colony, findG 0.

b FindGwhen: i n=3years ii n=10years iii n=30years.

c GraphGagainstn.

d Find the time it will take for the gorilla population to reach 200.

4 The weight of radioactive material in an ore sample aftertyears is given by

W=2: 3 £ 2 ¡^0 :^06 tgrams.

a Find the initial weight.

b Find the weight after: i 20 years ii 200 years iii 2000 years.

c GraphWagainstt.

d What is the percentage loss in weight from t=0to t=20?

e How long will it take for the weight to fall to 0 : 8 grams?

5 A cup of boiling water is placed in a refrigerator and aftertminutes its temperature is given by

T= 100£ 2 ¡

t 4 o

C.

a Find the inital temperature of the water.

b Find the water temperature after: i 2 minutes ii 10 minutes iii 1 hour.

c GraphTagainstt.

d There is no risk of the water causing scalding once its temperature falls to 49 oC. How long will

this take?

6 The value of an investment innyears’ time at 8 :3%p.a. compound interest is given by

a What was the original investment?

b Find the value of the investment after: i 3 years ii 10 years.

c Find the time taken for the value of the investment to double.

7 Aftermmonths, the value of a washing machine is given by V= 500(0:981)m dollars.

a What was the washing machine’s original value?

b How much is it worth after: i 6 months ii 4 years?

c How long will it take for the washing machine’s value to reduce to$150?

8 A bacteria population doubles every 1 : 5 days. Initially there are 20 bacteria.

a

b

c Find the number of bacteria after:

i 2 days ii 1 week iii 2 weeks.

d The presence of 5000 bacteria is considered dangerous. How long will it take the population to

reach this level?

9 Answer theOpening Problemon page 565.

F= 5800£(1:083)ndollars.

Exponential functions and equations (Chapter 28) 575

Find a formula for the number of bacteriaBafterddays.

Sketch the graph ofBagainstdfor the first 15 days.

IGCSE01

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Y:\HAESE\IGCSE01\IG01_28\575IGCSE01_28.CDR Tuesday, 18 November 2008 11:01:45 AM PETER