Rate of change of linear functions
Swimming pool

The entrance fee to the swimming pool is 3 dollars.
Two types of yearly subscriptions are also available:


Type of subscription Yearly fee Per-visit fee
"Thrifty Swimmer" $40 $1
"Free Swim" $100 free






The tool below shows the dependence of the yearly cost on the number of times a person visits the pool without any subscription.


Use the tool below to describe the dependence of the yearly cost on the number of visits to the pool for each of the two subscriptions (the costs involve both the subscription and the per-visit fee). Describe the change and use a correspondence rule.
  • Compare the three options (no subscription, "Thrifty Swimmer," and "Free Swim"), and present the functions that describe these options using the Representation of Functions tool. Use graphs or value tables to decide which option you would recommend to someone who visits the pool:
    - Once a month.
    - Once a week.
    - Every day.

  • Pool management is considering introducing another type of subscription with a $2 per-visit fee. What would you recommend as the yearly fee for this subscription? Explain your considerations. Under what conditions should a person choose this new subscription?


  • x visits y
    cost
    per-visit fee g slope of g
    yearly cost (dollars)
    number of visits per year
    grid
    subscription
    per-visit fee
    g






    Change at a constant rate

    Gym
    200-meter dash
    Wages
    Swimming pool
    Burning calories
    Growing hair
    Currency exchange
    Bank accounts
    Value tables and rate of change
    Rides
    Trips
    Constant and non-constant rate
    Graphs and correspondence rules

    Exercise 1
    Exercise 2
    Exercise 3
    Exercise 4
    Exercise 5