Growth and Decay

## Growth and Decay

Growth and Decay measures values which will either increase or decrease over time. This may be a simple increase or decrease, or it may be a compound increase or decrease.

To solve Growth and Decay problems:

Determine the starting value

For each iteration:

• Determine the input

• Work out the calculation

• Obtain the answer for that iteration

• The answer becomes the new input

until the number of iterations are complete.

## Example 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, in addition, 50 turns each minute. How many complete minutes does the flywheel take to stop?

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.

## Example 2

A weed in a river spreads by doubling the number of its plants each week, and starts with 1 weed. The local river authority can clear the number of weeds at the rate of 300 per week. If the local river authority starts treating the weed growth at the end of week 9, how many complete weeks will it be before the river is cleared?

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

Week 9: 256

Begin reduction of the weeds from week 10:

Week 10: 256 x 2 - 300 = 212

Week 11: 212 x 2 - 300 = 124

Week 12: 124 x 2 - 300 = -52