**Growth and Decay Problems**

Starter

Start on the left, work your way across doing the calculations in your head, and write down the answer.

START ANSWER

56 >> ÷ 8 , x 11 , + 13 , ÷ 5 , x 10 , - 4 , ÷ 11 , x 4 , - 19 ………….

48 >> ÷ 6 , x 9 , + 16 , ÷ 11 , x 9 , - 8 , ÷ 8 , x 4 , - 17 ………….

40 >> ÷ 5 , x 7 , + 14 , ÷ 5 , x 3 , - 6 , ÷ 6 , x 4 , - 13 ………….

32 >> ÷ 8 , x 12 , + 12 , ÷ 5 , x 7 , - 3 , ÷ 9 , x 5 , - 19 ………….

24 >> ÷ 3 , x 11 , + 12 , ÷ 5 , x 3 , - 4 , ÷ 7 , x 8 , - 29 ………….

Decay problems

A bouncing ball loses one-third of its height every bounce. The ball was originally dropped from a height of 2.7 metres. Work out the height the ball reaches after the 6th bounce. Give your answer to 2 decimal places.

Growth and Decay

The number of bacteria doubles every 5 hours. How many bacteria will there be after 100 hours if there are 2000 bacteria at the beginning?

Starter

Start on the left, work your way across doing the calculations in your head, and write down the answer.

START ANSWER

56 >> ÷ 8 , x 11 , + 13 , ÷ 5 , x 10 , - 4 , ÷ 11 , x 4 , - 19 ……45…….

48 >> ÷ 6 , x 9 , + 16 , ÷ 11 , x 9 , - 8 , ÷ 8 , x 4 , - 17 ……15…….

40 >> ÷ 5 , x 7 , + 14 , ÷ 5 , x 3 , - 6 , ÷ 6 , x 4 , - 13 ……11…….

32 >> ÷ 8 , x 12 , + 12 , ÷ 5 , x 7 , - 3 , ÷ 9 , x 5 , - 19 ……26…….

24 >> ÷ 3 , x 11 , + 12 , ÷ 5 , x 3 , - 4 , ÷ 7 , x 8 , - 29 ……35…….

Growth and Decay

The number of bacteria doubles every 5 hours. How many bacteria will there be after 100 hours if there are 2000 bacteria at the beginning?

2000 x 2 = 2097152000

20

**L.O. - Solve problems involving repeated growth and decay.**

Decay problems

A bouncing ball bounces to two-thirds of its original height after each bounce. The ball was originally dropped from a height of 2.7 metres. Work out the height the ball reaches after the 6th bounce. Give your answer to 2 decimal places.

2.7 x = 0.24 metres

2

3

6

Activity

Complete the growth and decay worksheet.

Activity

**Activities**

**Activity**

Answers

Answers

**Key**

Examples

Examples

Worked

Example

Worked

Example

Bright Spark:

You are going to be given money every day for a week. You have two choices about how to be given the money:

(i) On Monday you are given £100, and then every day you get £10 more than the previous day.

(ii) On Monday you are given £10, and then every day you get double the amount from the previous day.

(a) How much more do you get by taking option 2 than option 1?

(b) How much would the first amount on Monday have to be for option 1 to get you more than option 2?

(c) Can you find starting values for Monday that result in the same amount for both options?