Intro to De^v Questions

Question 5: Derivatives and Antiderivatives, the Graphical Expression

This is a Non-Calculator Question!

Part 1:

This question consists of two parts, one part is a first and second derivative graphing question. The second part of the question is a matching game, where their are 4 antiderivative or derivative functions which through the process of their graph shapes you must pinpoint that graph in the five graphs that are given, one graph remains with no pair in the end.

Part 2:
Consists of 4 functions and 5 graphs, in which contestants must match all of the corresponding functions with their respective graphs. Leaving one graph unpaired.

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Question 4: Exponential Rates and Normalville

Presently in the town of Normalville, there is a deepening concern. The town is at a brink of having to redevelop a new part of town. For every four new citizens that the Normalville population increases, the town miust build a new house. The town has not built any homes in the last five years as they do not know how many citizens have moved into Normalville. This data table gives the population of Normalville over the last five years period.

a) How many new homes must the town of Normalville build. Round to the nearest whole house.

b) Find an exponential function, that models the population data.

c) Normalville was able to recieve government funding to build more houses for the population increase in the next four years in Normalville. Find the amount of houses need based on data given. To the nearest whole house.

d) If the house cost is $ 23052.00 to build a house how much money does Normalville need to build those houses they need.

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Question 3: Antidifferentiation and the Flight Paths of Airplanes

The flight of the airplane can be modelled by a piece-wise function that includes three portions. They include the flight acceleration for take off, constant flight, and flight deceleration until landing. For each city-to-city flight, the airplane accelerates for 0.25 hours, decelerates for 2/3 hours and flies the remaining distance at a constant velocity.

A.) Using the given functions and coordinates for each section of the piece-wise function, find the functions s(t)1, s(t)2, and s(t)3.

B.) With the functions s(t)1, s(t)2, and s(t)3, discover which of the three flights (taking into account departure time and flight delays) would arrive in Mexico City first, from the city of Winnipeg. Be sure to show all of your work and the times at which each airplane will arrive at Mexico City (Neglect time zone changes for time).


Route information:

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Question 2: Volumes of Revolution and RC Cars!

When the area between the functions 4x^2 and 2x^3 is spun around the line x = -2, a washer-like solid is formed.

A.) Find the volume of the solid generated.

B.) If the numerical value of the solid's volume is equivalent to the battery life remaining in minutes for a remote controlled car, find the instantaneous velocity in ft/min of the RC car at the end of its battery life span given the following position function:

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Question 1: Related Rates and the Related Bicycle

On the countryside, lies an intersection of roads. 12 km North of the intersection is positioned Car A, moving north of the intersection at the rate of 90km/h. 6 km West of the intersection is positioned another Car B, moving towards the intersection at the rate of 72 km/h.

A.) Find the rate at which the distance, c, between cars A and B is increasing. Approximate your answer to the nearest hundreth.

B.) If the rate (dc/dt) at which the distance between vehicles A and B is increasing is numerically equivalent to the time required in hours for a bicycle to reach its destination, find the distance travelled by the bicycle given the following:

• S(t) = y
• S(0) = 4
  

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Conclusion of DEV

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