y = aˣ: Space & Astronomy Applications
Mathematics
Year 9
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A worksheet exploring exponential graphs of the form y = aˣ through space and astronomy contexts.
Topics covered:
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Full preview • 12 questions
y = aˣ: Space & Astronomy Applications
Subject: MathematicsGrade: Year 9
Name:
Date:
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Untitled Worksheet
Grade Year 9
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the value of y when a = 3 and x = 4 for the exponential equation y = aˣ.
[2 marks]2.
Plot the graph of y = 2ˣ for x from -2 to 2 on the grid.
[3 marks]3.
If the exponential function models the decay of a space probe's signal strength, and y = 100(0.8)ˣ, what is the signal strength after 3 units of time?
[3 marks]B
Problem Solving & Reasoning
Answer all questions with detailed explanations.
1.
A spaceship's population grows exponentially according to y = 200(1.05)ˣ. How long will it take for the population to double? Show your working.
[4 marks]2.
Explain why the graph of y = 0.5ˣ is decreasing and what this models in space applications.
[3 marks]C
Real-world Applications
Solve the following space and astronomy-related problems.
1.
The brightness of a star diminishes exponentially with distance according to y = 1000(0.6)ˣ. How bright is the star when the distance x = 5 units?
[2 marks]2.
A spaceship's fuel consumption follows y = 500(1.1)ˣ. If the ship consumes 100 units of fuel, approximately how many units of time have passed?
[3 marks]D
Challenge & Extension
Attempt these advanced questions. Show all your work.
1.
A satellite's signal strength is modeled by y = 1200(0.95)ˣ. Find the value of x when y decreases to 300.
[3 marks]2.
Describe how the graph of y = 2ˣ differs from y = 0.5ˣ in terms of growth and decay, and relate this to space phenomena.
[3 marks]E
Mixed Review
Answer the following questions testing different aspects of y = aˣ.
1.
Construct a graph of y = 3ˣ for x from -2 to 2 on the grid. Describe the key features of this graph.
[4 marks]2.
Identify a common mistake when students plot y = 2ˣ and suggest how to correct it.
[2 marks]F
Error Analysis
Review the errors below and correct the mistakes.
1.
A student models exponential decay with y = 100(1.2)ˣ, but the graph shows increasing y-values over time. Identify and explain the mistake.
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet