C3 (Modelling)
The model
C=12+0.25x
represents the cost, C, of parking for x hours.
State the meaning of the value 12.
Initial parking charge/start-up fee of $12.
The correlation coefficient for a data set is
r=0.81
Describe the relationship.
Strong positive linear association.
Determine the next term in the sequence:
7, 11, 15, 19, ...
23
A vehicle loses 18% of its value each year.
Identify the depreciation model that should be used.
Reducing value depreciation.
Define a vertex in a network.
A point or location within a network.
A model for the temperature of a drink is
T=85−3t
State the meaning of the gradient.
The temperature decreases by 3°C per minute.
A regression equation is
y=4.5x+12
Predict y when x=6
39
An arithmetic sequence has first term 5 and common difference 4.
Determine the 12th term.
T12=5+11(4)=49
An investment earns 7.2% p.a. compounded monthly.
Determine the values of i and n for a 5-year investment.
i=0.072/12=0.006
n=5×12=60
A network contains 8 vertices and 12 edges.
What does an edge represent?
A connection between two vertices.
A town's population is modelled by
P=25 000(1.02)t
Determine the population after 8 years.
P=25000(1.02)8
P≈29 287
A student uses a regression line to predict a person's mass from their height.
Explain why the prediction may not be exactly correct.
There is natural variation in the data and not all observations lie on the regression line.
The geometric sequence
3, 6, 12, 24,...
is shown.
Determine the 8th term.
T8=3(2)7=384
A person wishes to have $40 000 in 10 years.
Identify the finance model required to determine how much should be invested today.
Present Value.
A transport network is shown.
The shortest route from A to D is found to have a total weight of 36.
Interpret the meaning of the weight.
The total distance, cost or travel time along the shortest route is 36 units.
A model predicts a water tank contains 420L after 10 days.
The actual amount measured is 390L.
Calculate and interpret the residual.
Residual = 390−420=−30L
A scatterplot shows a strong positive association.
A new data point lies well away from the overall pattern.
Describe one effect this point could have on the regression model.
It may change the equation of the regression line and alter the correlation coefficient.
Determine the sum of the first 25 terms of the arithmetic sequence
8, 11, 14, 17,...
S25=25/2[2(8)+24(3)] =1100
A saver deposits $250 at the beginning of every month into an investment account.
Identify:
Answer:
A postal worker must travel along every street exactly once before returning to the starting point.
Identify the network concept required.
Euler circuit.
Two models have been proposed for annual production of a factory:
Model A: P=1500+180t
Model B: P=1500(1.08)t
After 15 years, which model predicts greater production?
Model A:4200
Model B:1500(1.08)15≈4758
Model B predicts greater production.
A regression equation relating study time (x) and test score (y) is
y=12+8.5x
A student studies for 12 hours.
Explain whether using the equation to predict the student's score is appropriate if all collected data were between 1 and 7 hours of study.
Not appropriate.
The prediction involves extrapolation beyond the domain of the observed data, so the result may not be reliable.
A theatre has 20 seats in the first row.
Each subsequent row contains 3 more seats than the previous row.
Determine the total number of seats in the first 30 rows.
a=20 d=3
S30=30/2[2(20)+29(3)] =1905
A trust fund is established to provide a scholarship of $6000 every year forever.
The fund earns 4% p.a.
Determine the minimum amount required to establish the fund.
P=6000/0.04P=150,000
A salesperson must visit every town exactly once before returning to the starting town.
Identify the network problem and explain why a shortest-path algorithm is not sufficient.