A parking garage charges $5 for the first hour, $10 for up to 2 hours, and $12 for the entire day. Let G be the dollar cost of parking for t hours

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1 answer

To express the dollar cost G of parking in terms of hours t, we need to consider the different pricing brackets established by the parking garage:

  1. For the first hour (0 < t ≤ 1):

    • The cost is $5.
    • This can be expressed as: G(t)=5for 0<t1
  2. For up to 2 hours (1 < t ≤ 2):

    • The cost is a flat rate of $10.
    • This can be expressed as: G(t)=10for 1<t2
  3. For the entire day (t > 2):

    • The cost is an all-day fee of $12.
    • This can be expressed as: G(t)=12for t>2

Now we can combine these pieces into a piecewise function that describes the cost G(t) based on the value of t:

G(t)={5if 0<t1 10if 1<t2 12if t>2

Summary

Thus, the dollar cost G of parking for t hours is given by the piecewise function above, which covers all possible time intervals for parking based on the specified rates.