Growth and Decay

Growth and Decay

GCSE(F), GCSE(H),

Modelling is using Mathematics to determine what might happen under given circumstances. One use is to model Growth and Decay; that is, measuring a value which will either increase or decrease over time (or other measure). This may be a simple increase or decrease, or it may be a compound increase or decrease.

To solve Growth and Decay problems, construct a short algorithm or process:

Determine the Starting Value

For each iteration:

• Determine the input

• Work out the calculation

• Obtain the answer for that iteration

• Feed the answer back as the new input

Until the number of iterations are complete.

Examples

1. A flywheel (a wheel with momentum, designed to help an engine run more smoothly) is running at 500 revolutions per minute. Power to the flywheel is turned off. It slows down at the rate of 10% and 50 turns each minute. How many complete minutes does the flywheel take to stop?

Answer: 6 minutes

Start value: 500 rpm (revolutions per minute)

After 1 minute 500 - 10% of 500 - 50 = 400 rpm

After 2 minutes: 400 - 10% of 400 - 50 = 310 rpm

3 minutes = 229 rpm; 4 minutes: = 156.1 rpm; 5 minutes: = 90.5 rpm

6 minutes: 90.5 - 10% of 90.5 - 50 = 31.5 rpm. The flywheel will stop before the 7th minute.

2. A disease spreads by doubling the number of infected people each week, and starts with 1 infected person. The local health authority can clear the number of infected people at the rate of 300 cases a week. If the local health authority is notified at the end of week 9, how many complete weeks did the outbreak last?

Answer: 11 weeks

Double the number of people for the first 8 weeks: Week 0: 1, Week 1: 2, to Week 8: 128

Week 9: 256

Begin reduction as treatment takes place for week 10:

Week 10: 256 x 2 - 300 = 212

Week 11: 212 x 2 - 300 = 124

Week 12: 124 x 2 - 300 = -52