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Linear Models Introduction
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Linear Models Introduction
Show your working where needed. Use dollars and units in your answers.
Understanding Linear Models
1.A bike tour charges $7.20 for each kilometre travelled, plus a one-off $9 hire fee. Which rule gives the total charge C for a trip of d kilometres?
- C = 7.20d + 9
- C = 9d + 7.20
- C = 7.20 + 9 + d
- C = (7.20 + 9)d
2.For a straight-line rule written as y = mx + c, state what m and c tell you about the line.
3.Select every situation that can be represented by a linear model.
- A streaming subscription with a fixed monthly fee and a constant charge for each movie rented
- A colony of yeast that triples in size every hour
- A kayak rental charged at a fixed rate per hour, with no starting fee
- A car travelling at a steady speed
4.A climbing centre charges $24 per hour plus a $6 equipment fee. Use C = 24h + 6 to find the total cost for each hire duration.
Hire time (h)
Total cost (C)
1
$_____
2
$_____
4
$_____
Creating and Interpreting Linear Models
5.A rainwater tank holds 720 litres and loses water at a steady rate of 32 litres per minute. Write a rule for the amount of water W remaining after t minutes.
6.Use your rule from the previous question to calculate how much water remains in the tank after 15 minutes.
7.A monthly data plan costs $38, with an extra $1.10 per gigabyte used. If a bill is $57.80, how many gigabytes were used?
8.A temperature rises steadily over time t. At t = 0 hours, the temperature is 12°C, and at t = 4 hours, it is 24°C. Write an equation for the temperature T, find the temperature at 4 hours, and state when it reaches 30°C.
Real-World Applications
9.An electrician charges a $95 call-out fee and $72 for each hour of work. Write a linear model for the total cost C after h hours. Explain what the gradient and the y-intercept mean in this situation.
10.Two internet plans charge different rates. Plan A costs $32 per month plus $0.70 per gigabyte, while Plan B costs $20 per month plus $1.30 per gigabyte. Write a rule for each monthly cost and find the data use at which the plans cost the same.
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