ww2: problem 23 (1 point) you have only one attempt for this question. a parking lot charges $5 for the…
ww2: problem 23 (1 point) you have only one attempt for this question. a parking lot charges $5 for the first hour (or part of an hour) and $3 for each succeeding hour (or part), up to a daily maximum of $30. so, for example, a person who parks for 30 minutes owes $5, and a person who parks for 70 minutes owes $8. let f(t) be the amount owed after parking for t minutes. is this function continuous? select answer (if there are discontinuities, think about their significance to someone who parks in the lot).
Answer
Explanation:
Step1: Analyze cost - time relationship
The cost function $f(t)$ has different rules for different time intervals. For $0 < t\leq60$, $f(t) = 5$. When $60 < t\leq120$, $f(t)=5 + 3$, when $120 < t\leq180$, $f(t)=5 + 3\times2$ and so on until it reaches the maximum of $30$.
Step2: Check continuity at integer - hour intervals
Consider the limit as $t$ approaches $60$ from the left, $\lim_{t\rightarrow60^{-}}f(t)=5$. The limit as $t$ approaches $60$ from the right, $\lim_{t\rightarrow60^{+}}f(t)=5 + 3=8$. Since $\lim_{t\rightarrow60^{-}}f(t)\neq\lim_{t\rightarrow60^{+}}f(t)$, the function is discontinuous at $t = 60,120,180,\cdots$ (integer - hour multiples).
Answer:
No