1. Exponential graphs Grade 8
Recognise, sketch and interpret graphs of exponential functions y = kx for positive k
Plot and interpret exponential real-life graphs to find approximate solutions to real life problems
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2. Lesson Plan Lesson Overview Progression of Learning
Objective(s)
Recognise, sketch and interpret graphs of exponential functions y = kx for positive k
Plot and interpret exponential real-life graphs to find approximate solutions to real life problems
Grade 8
Prior Knowledge
Indices
Solving equations
Duration
40 minutes
Resources
Print slides:
Equipment
Progression of Learning
What are the students learning?
How are the students learning? (Activities & Differentiation)
Features of exponential graphs
Give students slide 15 printed. Using slides 4 and 5. Discuss the key features of exponential graphs. 5
Plotting an exponential graph
Demonstrate how to plot using slide 6. Students to plot y = 4x.
Practice recognise, sketch and interpret graphs and solving exponential functions.
Give students slide 16, 17 and 18. Complete practice questions related to the different aspects of exponential graphs.
Give students slide 19 – contextualised exponential grow question. Solution on slide 11 and 12. 20
Exponential graphs in exam questions (from specimen papers)
Give students slide 20. This includes 2 exam questions related to objective. Students to use notes from lesson. Ensure that all steps are shown. Relate to mark scheme to show how the marks are allocated. 10
Next Steps
Assessment
PLC/Reformed Specification/Target8/Algebra/Exponential Graphs

3. Key Vocabulary
Exponential Function Asymptote

4. y = 2x Exponential Graphs y x
Equations that have the form y = kx where k is a positive number are called exponential functions
All exponential graphs go through
the point (0,1) as any number to
the power zero is 1 y x

5. y = 10x Exponential Graphs y x
As k increases, the gradient of the graph becomes steeper. The value of y increases steeply as x increases.
y = 10x y x
As the value of x decreases, the graph gets closer and closer to the negative x axis but never touches the negative x axis. Thus, the negative x axis is an asymptote to the graph.

6. Drawing Exponential Graphs
Complete the table and draw the graph for the function y = 2x x -4 -3 -2 -1 1 2 3 4
y=2x
0.06
0.13
0.25
0.5 8 16 x y

7. Drawing Exponential Graphs
Complete the table and draw the graph for the function y = 4x x -3 -2 -1 1 2 3
y=2x
0.0625 16
0.0156
0.25 4 64

8. Match each graph to its equation
Practice - 1
Match each graph to its equation
y = 3x
y = 2-x
y = 5x
y = (1/4)x D A C B

9. Practice - 2 n = 5 x 20 n = 5 x 1 n = 5 n = 5 x 26 n = 5 x 64 n = 320
5000 < 5 x 2y
210 = 1024
29 = 512
10 years to exceed 5000
1000 < 2y

10. Practice - 3 100 = m x n2 25 = m x n0 25 = m x 1 100 = 25 x n2 25 = m
5 = p x q1
320 = p x q4
5 = p x q
320 = 5 x q4 q
5 = p q
320 = 5 x q3
64 = q3
4 = q
5 = p = 1.25 q

11. Problem Solving and Reasoning
The population of a planet which is currently at two thousand, is growing at a rate of 3 per cent per annum.
Show that the equation of the expected population, y thousands, in x years time, is given by y = 2 x 1.03x
Draw the graph of y = 2 x 1.03x for 0 ≤ x ≤ 50
Use your graph to estimate the population in 30 years’ time
d) Use your graph to estimate the time taken for the population to reach eight thousand.
Current population is at x=0. y = 2 x =2. So the current population is 2 and the multiplier for 3% growth is 1.03

12. Problem Solving and Reasoningy
y = 2 x 1.03x
Population in thousands
c)4.85
thousand x
d)47 years
Time (years)

13. Exam Question – Specimen Papers

14. Exam Question – Specimen Papers

15. Exponential Graphs Features: X -3 -2 -1 1 2 3 y=2x 0.0625 16
Complete the table and draw the graph for the function y = 4x X -3 -2 -1 1 2 3
y=2x
0.0625 16
Student Sheet 1

16. Match each graph to its equation
Practice - 1
Match each graph to its equation
y = 3x
y = 2-x
y = 5x
y = (1/4)x
Student Sheet 2

17. Practice - 2
Student Sheet 3

18. Practice - 3
Student Sheet 4

19. Problem Solving and Reasoning
The population of a planet which is currently at two thousand, is growing at a rate of 3 per cent per annum.
Show that the equation of the expected population, y thousands, in x years time, is given by y = 2 x 1.03x
Draw the graph of y = 2 x 1.03x for 0 ≤ x ≤ 50
Use your graph to estimate the population in 30 years’ time
d) Use your graph to estimate the time taken for the population to reach eight thousand.
Student Sheet 5

20. Exam Question – Specimen Papers
Student Sheet 6