Two variables, x and y, are connected by the equation y = kx^n - Scottish Highers Maths - Question 7 - 2022
Question 7
Two variables, x and y, are connected by the equation y = kx^n.
The graph of log_y against log_x is a straight line as shown.
Find the values of k and n.
Worked Solution & Example Answer:Two variables, x and y, are connected by the equation y = kx^n - Scottish Highers Maths - Question 7 - 2022
Step 1
Introduce logs to y = kx^n
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Answer
Take the logarithm of both sides:
extlogy​=extlog(k)+nextlog(x)
This represents a straight line with a slope of n and y-intercept of log(k) when plotted.
Step 2
Interpret intercept from the graph
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Answer
From the graph, the y-intercept occurs at (0, 3). Therefore,
extlog(k)=3
This implies that:
k=103=1000.
Step 3
Interpret gradient from the graph
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Answer
The gradient of the line is given as -2. Therefore,
n=−2.
Step 4
State k and n
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Answer
The values are:
k = 1000
n = -2
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