Traffic flow is defined as the rate at which cars pass through an intersection, measured in cars per minute. The traffic flow at a particular intersection is modeled by the function $F$ defined by $$F ( t ) = 82 + 4 \sin \left( \frac { t } { 2 } \right) \text { for } 0 \leq t \leq 30$$ where $F ( t )$ is measured in cars per minute and $t$ is measured in minutes. (a) To the nearest whole number, how many cars pass through the intersection over the 30 -minute period? (b) Is the traffic flow increasing or decreasing at $t = 7$ ? Give a reason for your answer. (c) What is the average value of the traffic flow over the time interval $10 \leq t \leq 15$ ? Indicate units of measure. (d) What is the average rate of change of the traffic flow over the time interval $10 \leq t \leq 15$ ? Indicate units of measure.
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Traffic flow is defined as the rate at which cars pass through an intersection, measured in cars per minute. The traffic flow at a particular intersection is modeled by the function $F$ defined by
$$F ( t ) = 82 + 4 \sin \left( \frac { t } { 2 } \right) \text { for } 0 \leq t \leq 30$$
where $F ( t )$ is measured in cars per minute and $t$ is measured in minutes.
(a) To the nearest whole number, how many cars pass through the intersection over the 30 -minute period?
(b) Is the traffic flow increasing or decreasing at $t = 7$ ? Give a reason for your answer.
(c) What is the average value of the traffic flow over the time interval $10 \leq t \leq 15$ ? Indicate units of measure.
(d) What is the average rate of change of the traffic flow over the time interval $10 \leq t \leq 15$ ? Indicate units of measure.