The graph shows the populations of two different animals, W and K, in a conservation park over time - HSC - SSCE Mathematics Advanced - Question 13 - 2024 - Paper 1
Question 13
The graph shows the populations of two different animals, W and K, in a conservation park over time. The y-axis is the size of the population and the x-axis is the n... show full transcript
Worked Solution & Example Answer:The graph shows the populations of two different animals, W and K, in a conservation park over time - HSC - SSCE Mathematics Advanced - Question 13 - 2024 - Paper 1
Step 1
Population in 1985
96%
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Answer
For Population K, we are given that it is represented by B. Since population W's initial size in 1985 is A = 34, we can establish that B must be 280, as shown in the marking scheme.
Step 2
Percentage yearly change in the population
99%
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Answer
Population W has a growth factor of 1.055 per year, indicating a percentage increase of 5.5%. Population K, with a decay factor of 0.97, has a percentage decrease of 3%.
Step 3
Population when x = 50
96%
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Answer
To find the population of W when x = 50, we use the formula:
P=34×(1.055)50
Calculating this gives:
34×494.426≈494
Thus, the population of W when x = 50 is approximately 494. For population K, the problem states the predicted population is 61.
