A parking garage charges 2 for up to (but not including) 1 hr of parking, 4 for up to 2 hr of

Name: Problem 69, Chapter 2: Precalculus: A Right Triangle Approach
Uploaded: 2020-07-31T19:54:20-08:00
Duration: 1 min 41 s
Channel: Ankit Gupta
Description: A parking garage charges 2 for up to (but not including) 1 hr of parking, 4 for up to 2 hr of parking, 6 for up to 3 hr of parking, and so on. Let C(t)= the cost of parking for t hours. a) Graph the function. b) Write an equation for C(t) using the greatest integer notation t .

step 1 cost of parking is given as $2 when the time is between 1 hour and greater than 0. This is $4 wh

Question

A parking garage charges $\$ 2$ for up to (but not including) $1 \mathrm{hr}$ of parking, $\$ 4$ for up to $2 \mathrm{hr}$ of parking, $\$ 6$ for up to $3 \mathrm{hr}$ of parking, and so on. Let $C(t)=$ the cost of parking for $t$ hours. a) Graph the function. b) Write an equation for $C(t)$ using the greatest integer notation $\llbracket t \rrbracket$.

   A parking garage charges $\$ 2$ for up to (but not including) $1 \mathrm{hr}$ of parking, $\$ 4$ for up to $2 \mathrm{hr}$ of parking, $\$ 6$ for up to $3 \mathrm{hr}$ of parking, and so on. Let $C(t)=$ the cost of parking for $t$ hours.
a) Graph the function.
b) Write an equation for $C(t)$ using the greatest integer notation $\llbracket t \rrbracket$.

Precalculus: A Right Triangle Approach

Judith A. Beecher,… 4th Edition

Chapter 2, Problem 69

Instant Answer

Solved by Expert Ankit Gupta

07/31/2020

Step 1

The parking garage charges in increments of $2$ dollars for each hour or part thereof. Specifically, the cost is $2$ dollars for less than 1 hour, $4$ dollars for at least 1 hour but less than 2 hours, $6$ dollars for at least 2 hours but less than 3 hours, and so Show more…

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A parking garage charges $\$ 2$ for up to (but not including) $1 \mathrm{hr}$ of parking, $\$ 4$ for up to $2 \mathrm{hr}$ of parking, $\$ 6$ for up to $3 \mathrm{hr}$ of parking, and so on. Let $C(t)=$ the cost of parking for $t$ hours. a) Graph the function. b) Write an equation for $C(t)$ using the greatest integer notation $\llbracket t \rrbracket$.

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Key Concepts

Piecewise Functions

Piecewise functions are defined by different rules over different intervals of their domain. They are essential in modeling scenarios where a relationship or rule changes at specific points, such as in tariff systems where different charges apply over distinct time ranges.

Greatest Integer Function (Floor Function)

The greatest integer function, often denoted by ?t?, returns the largest integer that is less than or equal to a given number t. This function is key to representing the discrete jump changes in piecewise functions, especially in contexts where continuous variables are mapped to discrete outcomes.

Graphing Step Functions

Graphing step functions involves plotting segments in which the function has a constant value over intervals, with discontinuities or jumps at the interval boundaries. This concept is crucial for visually understanding functions that exhibit sudden changes in value, such as cost functions in pricing models.

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