# Exponential Growth Formula

In this worksheet, students answer wordy questions on exponential growth 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 growth 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 growth factor

x = time

Example

The rabbit population in a farmer's field increases by 20% each year.  There are currently about 50 rabbits in the field.  If the farmer does nothing about the rabbits, how many will there be in 4 years?

a = 50

b = 20% = 0.20 = 0.2

x = 4

y = a(1 + b)x = 50 (1.2)4 = 103.68

There will be roughly 104 rabbits.

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

If the farmer does nothing about the badgers, how many will there be in 10 years time?

Car prices are expected to rise by 5% each year.

The current price of a new car is £15000

How much is the price of this car expected to be in 4 years time?

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

The population of a certain town is expected to rise by 10% 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 integer)

The rabbit population in a farmer's field increases by 25% each year.

There are currently about 50 rabbits in the field.

If the farmer does nothing about the rabbits, how many will there be in 5 years?

Car prices are expected to rise by 8% each year.

The current price of a new car is £17000

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

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

Inflation is estimated to be at 2.8%.

If a book costs £10 now, how much is it expected to cost in 5 years' time?

(Just give your answer as a number in £s to the nearest penny)

As a company expands, it uses 12% more electricity each year.

It currently uses 100000 KWh per year.

What is the estimated usage in 3 years' time?

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

The population of Newberry Town is 12000.  It is expected to increase 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)

A bank pays 4% interest.

If I invest £100 now, how many years will it take for me to double my money at this fixed rate?

10 years

17 years

18 years

25 years

A bank pays 10% interest.

If I invest £100 now, how many years will it take for me to double my money at this fixed rate?

5 years

7 years

8 years

10 years

• Question 1

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

If the farmer does nothing about the badgers, how many will there be in 10 years time?

26
EDDIE SAYS
10 × (1 + 0.10)10
• Question 2

Car prices are expected to rise by 5% each year.

The current price of a new car is £15000

How much is the price of this car expected to be in 4 years time?

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

£18233
18233
EDDIE SAYS
15000 × (1 + 0.05)4
• Question 3

The population of a certain town is expected to rise by 10% 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 integer)

62250
EDDIE SAYS
24000 × (1 + 0.10)10
• Question 4

The rabbit population in a farmer's field increases by 25% each year.

There are currently about 50 rabbits in the field.

If the farmer does nothing about the rabbits, how many will there be in 5 years?

153
EDDIE SAYS
50 × (1 + 0.25)5
• Question 5

Car prices are expected to rise by 8% each year.

The current price of a new car is £17000

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

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

£29135
29135
EDDIE SAYS
17000 × (1 + 0.08)7
• Question 6

Inflation is estimated to be at 2.8%.

If a book costs £10 now, how much is it expected to cost in 5 years' time?

(Just give your answer as a number in £s to the nearest penny)

£11.48
11.48
EDDIE SAYS
10 × (1 + 0.028)5
• Question 7

As a company expands, it uses 12% more electricity each year.

It currently uses 100000 KWh per year.

What is the estimated usage in 3 years' time?

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

140493
EDDIE SAYS
100000 × (1 + 0.12)3
• Question 8

The population of Newberry Town is 12000.  It is expected to increase 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)

36000
EDDIE SAYS
12000 × (1 + 0.045)25
• Question 9

A bank pays 4% interest.

If I invest £100 now, how many years will it take for me to double my money at this fixed rate?

18 years
EDDIE SAYS
1.0417 = 1.9479...
1.0418 = 2.0258...
• Question 10

A bank pays 10% interest.

If I invest £100 now, how many years will it take for me to double my money at this fixed rate?

8 years
EDDIE SAYS
1.107 = 1.9487...
1.108 = 2.1435...
---- OR ----

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