Exponential Decay Formula

In this worksheet, students answer wordy questions on exponential decay using the formula.

Key stage:  KS 4

Curriculum topic:  Ratio, Proportion and Rates of Change

Curriculum subtopic:  Set Up, Solve and Interpret Answers in Growth and Decay Problems

Difficulty level:

QUESTION 1 of 10

The formula for exponential decay is:

y = a(1 - b)x

where

y = the final amount

a = the original amount

b = the percentage change as a decimal, so 1 + b is the decay factor

x = time

Example

The coal stock at a mine decreases by 20% each year.  There are currently about 5 million tons left at the mine.  How much coal will be left in 10 years' time?

a = 5000000

b = 20% = 0.20 = 0.2

x = 10

y = a(1 - b)x = 5000000 (0.8)10 = 536871

There will be roughly 537000 tons.

The badger population in a farmer's field decreases by 10% each year.

How many will there be in 10 years' time?

Computer prices are expected to fall by 5% each year.

The current price of a new computer is £1500.

How much is the price of a similar computer expected to be in 3 years' time?

(Just give your answer as a number rounded to the nearest pound)

The population of a certain rural town is expected to fall by 9% each year.

The current population of the town is 24000.

What is the estimated population in 10 years' time?

(Just give your answer as a number rounded to the nearest hundred)

The butterfly population in a field decreases by 25% each year.

There are currently about 500 butterflies in the field.

How many will there be in 5 years?

The value of a certain car is expected to fall by 12% each year.

The current value of a car is £19000

How much is the value of this car expected to be in 7 years' time?

(Just give your answer as a number rounded to the nearest pound)

The population of Oldberry Town is 12000.  It is expected to decrease by 4½% each year.

What is the predicted population in 25 years' time?

(Just give your answer as a number rounded to the nearest thousand)

Computer software prices are expected to fall by 10% each year.

After how many years would you expect prices to be half of today's prices.

4 years

5 years

6 years

7 years

The population of a certain town is expected to fall by 10.5% each year.

The current population of the town is 30000.

What is the estimated population in 7 years' time?

(Just give your answer as a number rounded to the nearest hundred)

The population of a certain country is expected to fall by 2.4% each year.

The current population of the country is 35 million.

What is the estimated population in 30 years' time?

(Just give your answer as a number rounded to the nearest million)

The population of a certain species is expected to fall by 8.5% each year.

After how many years will the population be halved?

7 years

8 years

9 years

10 years

• Question 1

The badger population in a farmer's field decreases by 10% each year.

How many will there be in 10 years' time?

35
EDDIE SAYS
100 × (1 - 0.10)10
• Question 2

Computer prices are expected to fall by 5% each year.

The current price of a new computer is £1500.

How much is the price of a similar computer expected to be in 3 years' time?

(Just give your answer as a number rounded to the nearest pound)

£1286
1286
EDDIE SAYS
1500 × (1 - 0.05)3
• Question 3

The population of a certain rural town is expected to fall by 9% each year.

The current population of the town is 24000.

What is the estimated population in 10 years' time?

(Just give your answer as a number rounded to the nearest hundred)

9300
EDDIE SAYS
24000 × (1 - 0.09)10
• Question 4

The butterfly population in a field decreases by 25% each year.

There are currently about 500 butterflies in the field.

How many will there be in 5 years?

120
EDDIE SAYS
500 × (1 - 0.25)5
• Question 5

The value of a certain car is expected to fall by 12% each year.

The current value of a car is £19000

How much is the value of this car expected to be in 7 years' time?

(Just give your answer as a number rounded to the nearest pound)

£7765
7765
EDDIE SAYS
19000 × (1 - 0.12)7
• Question 6

The population of Oldberry Town is 12000.  It is expected to decrease by 4½% each year.

What is the predicted population in 25 years' time?

(Just give your answer as a number rounded to the nearest thousand)

4000
EDDIE SAYS
12000 × (1 - 0.045)25
• Question 7

Computer software prices are expected to fall by 10% each year.

After how many years would you expect prices to be half of today's prices.

7 years
EDDIE SAYS
0.96 = 0.5314...
0.97 = 0.4782...
• Question 8

The population of a certain town is expected to fall by 10.5% each year.

The current population of the town is 30000.

What is the estimated population in 7 years' time?

(Just give your answer as a number rounded to the nearest hundred)

13800
EDDIE SAYS
30000 × (1 - 0.105)7
• Question 9

The population of a certain country is expected to fall by 2.4% each year.

The current population of the country is 35 million.

What is the estimated population in 30 years' time?

(Just give your answer as a number rounded to the nearest million)

17000000
EDDIE SAYS
35000000 × (1 - 0.024)30
• Question 10

The population of a certain species is expected to fall by 8.5% each year.

After how many years will the population be halved?