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Exponential Growth Formula

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

'Exponential Growth Formula' worksheet

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:  

down

Worksheet Overview

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?

 

Answer

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. 

 

There are currently about 10 badgers in the field. 

 

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. 

 

There are currently about 10 badgers in the field. 

 

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

CORRECT ANSWER
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)

CORRECT ANSWER
£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)

CORRECT ANSWER
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?

CORRECT ANSWER
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)

CORRECT ANSWER
£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)

CORRECT ANSWER
£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)

CORRECT ANSWER
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)

CORRECT ANSWER
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?

CORRECT ANSWER
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?

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

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