Automobile traffic passes a point P on a road of width w feet with an average rate of R vehicles per second. Although the arrival of automobiles is irregular, traffic engineers have found that the average waiting time T until there is a gap in traffic of at least 1 seconds is approximately T = teRt seconds. A pedestrian walking at a speed of 3.3 ft/s requires t = s to cross the road. Therefore, the average time the pedestrian will have to wait before crossing is f(w, R)= () ew R/3.3 s What is the pedestrian's average waiting time if w = 24 ft and R = 0.2 vehicle per second?

Use the table of values you made in part 4 of the example to find the limiting value of the average rate of change in velocity.

2. The graph shows the population of bacteria in a culture. Please help me! A) Determines the average rate of crop variation between the 3rd and 4th hour. B) What does this rate of change mean?

Consider a television camera positioned 1 km from the base of a launching pad and that the rocket is rising vertically at constant speed. Imagine the angle of the camera is always adjusted in a way to keep it aimed at the rocket. As the rocket rises, the angle of the camera Eventually stops increasing completely. Keeps increasing and has too change each time faster and faster. Keeps increasing but can change each time slower and slower. Increases at first, but then starts to decrease after some time. Page 5 of 7

y = 53452634Xexp(0.0518X(x-1975)) x= years   deep analysis why expoetinal model would be more valid than linear for this data and what are some limitatios of it/

MI Y21 41 PIZ 28) (a) Is the graph pictured below a function? 4 A زفاده -2 B -1 1 0 -1- -2- -3- 0 3 1 Why or why not. (b) What is the average rate of change from B to C? S

The following table gives data for the velocity of a sports car accelerating from 0 to 193 miles per hour over the course of 36 seconds (10 thousandths of an hour).

Much of Trail Ridge Road in Rocky Mountain National Park is over 12,000 feet high. Although it is a beautiful drive in summer months, in winter the road is closed because of severe weather conditions. Sustained gale-force winds (over 32 miles per hour and often over 90 miles per hour) occur on the average of once every 65 hours at a Trail Ridge Road weather station. (a) Letr = frequency with which gale-force winds occur in a given time interval. Explain why the Poisson probability distribution would be a good choice for the random variable r. O Frequency of gale-force winds is a common occurrence. It is reasonable to assume the events are dependent. O Frequency of gale-force winds is a common occurrence. It is reasonable to assume the events are independent. O Frequency of gale-force winds is a rare occurrence. It is reasonable to assume the events are dependent. O Frequency of gale-force winds is a rare occurrence. It is reasonable to assume the events are independent. (b) For an…

Find expressions for marginal revenue in the case when the demand equation is given by 1000 (a) P= \(100 – 2Q) (b) P = (2 + Q)

Suppose the odometer on our car is broken and we want to estimate the distance driven over a 30 second time interval. We take the speedometer readings every five seconds and record them in the following table. Time (s) 0 5 15 20 25 30 Velocity (mi/h) 17 21 24 29 32 31 28 In order to have the time and the velocity in consistent units, let's convert the velocity readings to feet per second (1 mi/h Time (s) Velocity (ft/s) DA 40+ 20- 0 5 25 40- 10 ft. If we add similar estimates for the other time intervals, we obtain an estimate for the total distance traveled. (25 x 5) + (31 x 5) + (35 × 5) + (43 × 5) + (47 × 5) + (45 × 5) = ft. 20- 10 35 During the first five seconds the velocity doesn't change very much, so we can estimate the distance traveled during that time by assuming that the velocity is constant. If we take the velocity during that time interval to be the initial velocity (25 ft/s), then we obtain the approximate distance traveled during the first five seconds. 25 ft/s x 5 s ft…