Which of the following best represents the graph of $y = 10(0.8)^x$?
A - HSC - SSCE Mathematics Standard - Question 10 - 2021 - Paper 1
Question 10
Which of the following best represents the graph of $y = 10(0.8)^x$?
A.
B.
C.
D.
Worked Solution & Example Answer:Which of the following best represents the graph of $y = 10(0.8)^x$?
A - HSC - SSCE Mathematics Standard - Question 10 - 2021 - Paper 1
Step 1
Analyze the equation $y = 10(0.8)^x$
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Answer
This equation represents an exponential function where the base is 0.8, indicating that the function is decreasing as x increases. The coefficient 10 indicates that the graph starts at y=10 when x=0. As x approaches positive infinity, y will approach 0.
Step 2
Identify key characteristics of the graph
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Answer
Since the base is less than 1, the graph will start high and decline towards the x-axis, but never touching it. The value at x=0 is y=10, and as x increases, y will decrease but remain positive.
Step 3
Compare with provided graphs
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Answer
The correct graph should start at y=10 and show a decreasing trend towards the x-axis without crossing it. Option A is the only option that accurately represents this behavior.
