Exponential Growth and Decay

Before we start this work it is helpful to remember our work on compound interest/depreciation.

We are going to flick through the slides for two questions we have done in the past. Discussing the ideas to remember what we already know.

Lets remember this style of question …..You invest £2000 in a bank. They are offering 8%. You leave your money there for 5 years.How much do you have at the end of 5 years. (4 marks)

Work out the interest rate as a decimal

Work out the MULTIPLIER

Draw a table

Complete the table

Year Start Multiplier End

1

2

3

4

2000 2160

2160 2332.8

2332.8 1.08 2519.424

2519.424 2720.97791.08

1.08

1.08

Final Answer = £2 720.98

Lets think about the quick way

Taking it further – Depreciation ….3) Anna bought a car for £8 500. The car depreciates at a rate of 11% per year.

Work out how much the car is worth in 4 years time.

Work out the depreciation rate as a decimal

Work out the MULTIPLIER – it will be 1 – depreciation rate.

Draw a table

Complete the table.

Year Start End1 8500234

7565

7565 6732.85

6732.85 5992.2365

5992.2365 5333.090485

£ 5 333.09

Lets think about the quick way

These ideas can be applied to topics that are not just about money. Let’s see if we can apply these thoughts/this knowledge to other ideas……

A population of bacteria increases by 60% every hour.

a)Copy and complete this table of values.

b)Draw a graph of the number of bacteria against time.

Time (hours) 0 1 2 3 4 5Number of bacteria

1000

Lets think about how we are going to round the numbers that we put into the

table

Drawing the graph requires some thought about the

scales

B/A standard work

a) At the end of each hour, the number of bacteria will be 160% of the number at thebeginning of that hour.The multiplier = 1.60 = 1.6 for each hourAt each stage, continue theAfter 1 hour there will be 1000 X 1.6 = 1600 bacteria. working on your calculatorAfter 2 hours there will be 1600 X 1.6 = 2560 bacteria. rather than starting again.After 3 hours there will be 2560 X 1.6 = 4096 bacteria and so on.The table gives the number of bacteria after each hour, with values rounded to thenearest whole number where necessary.

Solution to the question from before

Solution to the question from before

When you have completed the graph you need to work on questions 4,5,6, and 7 from the text book

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