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Which equation best represents this graph? A - HSC - SSCE Mathematics Extension 1 - Question 7 - 2018 - Paper 1
Question 7
Which equation best represents this graph? A. P(t) = 1500 + 1500e^{-kt} B. P(t) = 3000 - 1500e^{-kt} C. P(t) = 3000 + 1500e^{-kt} D. P(t) = 4500 - 1500e^{-kt}
Worked Solution & Example Answer:Which equation best represents this graph? A - HSC - SSCE Mathematics Extension 1 - Question 7 - 2018 - Paper 1
Step 1
Identify the Graph Characteristics
Answer
The graph likely demonstrates a population or quantity that starts at a certain value and approaches a horizontal asymptote as time increases. This is indicative of an exponential growth or decay model.
We need to determine the starting point and behavior of the function.
Step 2
Analyze Each Option
Answer
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Option A: P(t) = 1500 + 1500e^{-kt}
- This suggests that the minimum value is 1500, but does not lead to a sufficient maximal value as it adds the exponential term to the constant.
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Option B: P(t) = 3000 - 1500e^{-kt}
- This starts at 3000 and decreases as time increases, which does not align with typical population growth characteristics.
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Option C: P(t) = 3000 + 1500e^{-kt}
- This starts at 3000 and increases towards a maximum asymptote of 4500 as time increases, showing growth.
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Option D: P(t) = 4500 - 1500e^{-kt}
- This starts at a constant of 4500 and decreases, which contradicts the expected growth behavior.
Step 3