IB myp 4-5 MATHEMATICS – Practice Questions- All Topics
Topic :Functions-Calculating network pathways
Topic :Function- Weightage : 21 %
All Questions for Topic : Representation and shape of more complex functions,Transformation of quadratic functions,Rational functions,Graphing trigonometric functions,Linear programming, including inequalities,Networks-edges and arcs, nodes/ vertices, paths,Calculating network pathways,Weighted networks,Domain and range
Question
In this question you will interpret information to discuss the sustainability of a proposed airport development.
 |  |  |
The airport employment data for 2013 in Tab 1 shows the relationship between the number of jobs at the airport $(y)$ and the number of passengers $(x)$ through the airport in millions. The line of best fit is represented by the equation:
$$
y=2110 x-52818 .
$$
Question (a)
The number of jobs at Hong Kong International Airport was 65000 in 2013. Use the equation of the line of best fit from Tab 1 to estimate the number of passengers passing through the airport. Round your answer to the nearest million.
▶️Answer/Explanation
Ans:
Given information:
Number of jobs at Hong Kong International Airport in $2013: 65,000$
Equation of the line of best fit:
\[ y = 2110x – 52818 \]
Here, \( y \) represents the number of jobs and \( x \) represents the number of passengers in millions.
Substituting \( y = 65,000 \) into the equation, we get:
\[ 65,000 = 2110x – 52818 \]
Adding 52,818 to both sides of the equation:
\[ 65,000 + 52,818 = 2110x \]
\[ 117,818 = 2110x \]
Dividing both sides by 2110:
\[ x = \frac{117,818}{2110} \approx 55.88 \]
Rounding the estimated number of passengers to the nearest million, we get:
Estimated number of passengers \( \approx 56 \) million
Question (b)
The actual number of passengers through Hong Kong International Airport was 68488000 . Calculate the percentage error of your rounded answer from part (a).
$$
\text { Percentage error }=\left|\frac{\text { rounded value }- \text { actual value }}{\text { actual value }}\right| \times 100 \%
$$
▶️Answer/Explanation
Ans:
To calculate the percentage error, we will use the rounded value from part (a) and the actual value of passengers passing through Hong Kong International Airport.
Rounded value: 56 million
Actual value: 68,488,000
Percentage error formula:
\[
\text{Percentage error} = \left|\frac{\text{rounded value} – \text{actual value}}{\text{actual value}}\right| \times 100\%
\]
Substituting the values into the formula:
\[
\text{Percentage error} = \left|\frac{56,000,000 – 68,488,000}{68,488,000}\right| \times 100\%
\]
Calculating the percentage error:
\[
\text{Percentage error} = \left|\frac{-12,488,000}{68,488,000}\right| \times 100\%
\]
\[
\text{Percentage error} \approx 18.22\%
\]
Therefore, the percentage error of the rounded answer from part (a) is approximately 18.22%.