Two variables, x and y, are connected by the equation y = kx^n - Scottish Highers Maths - Question 9 - 2017
Question 9
Two variables, x and y, are connected by the equation y = kx^n.
The graph of log_2 y against log_2 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 9 - 2017
Step 1
State linear equation
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
From the given equation, we can express it in a logarithmic form:
ext{Let } y &= kx^n \\
ext{Taking log on both sides:} \\
ext{log_2 y} &= ext{log_2(kx^n)} \\
&= ext{log_2 k} + n ext{log_2 x}
ext{This represents a linear equation of the form:} \\
ext{log_2 y} = n ext{log_2 x} + ext{log_2 k}
ext{where the gradient is } n ext{ and the y-intercept is log_2 k.}
\end{align*}$$
Step 2
Use the graph to find the y-intercept
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
From the graph, the y-intercept is at y = -12 when log_2 x = 0. Thus,
extlog2k=−12
To express k in exponential form, we rewrite:
k=2−12
Step 3
Identify the gradient from the graph
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
The gradient of the line from the graph is identified as 3. Thus,
n=3
Step 4
State k and n
98%
120 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Finally, combining our results gives:
k=2−12n=3
Join the Scottish Highers students using SimpleStudy...
