Complete the exercises listed below with the following requirements.
Solutions must be well-written.
Solutions should be in order.
Solutions should be written in black ink or typed.
If typed, the font should be at least 12 point.
Files should be submitted as a single pdf containing all solutions.
Criteria:
Each exercise will be graded using the project rubric below.
Project 1 Exercises
1. A boat travels at a constant speed of 3 miles per hour in still water. In a river with an unknown current, it takes the boat twice as long to travel 60 miles upstream (against the current) than it takes for the 60-mile return trip (with the current). What is the speed of the current in the river? Hint: s=vt.
2. A company that manufactures running shoes has a fixed monthly cost of $300000. It costs $30 to produce each pair of shoes.
Write the cost function, C(x), of producing x pairs of shoes.
Write the average cost function, C⎯⎯⎯(x), of producing x pairs of shoes.
Find and interpret C⎯⎯⎯(1000), C⎯⎯⎯(10000), and C⎯⎯⎯(100000).
3. The function f(x)=20(0.975)xis used to model the percentage of surface sunlight, f(x), that reaches a depth of x feet beneath the surface of the ocean. At what depth, to the nearest foot, is 1% of surface sunlight present?
4. The logistic function p(t)=10001+9e−0.6t models the population of a fish farm in t years. Determine the following.
The initial population of fish.
The doubling time for the population, to the nearest tenth.
The population of fish in two years, to the nearest integer.
The time it will take to reach 900 fish, to the nearest tenth.
The maximum capacity for the fish farm. Hint: You may want to use a graph to justify this.
5. The original formula for calculating the magnitude of an earthquake is M=log(II0). Solve for I.
6. Using the graph below, determine if you should use an exponential, logarithmic, or logistic model. Explain your answer. (Uploaded File)
7. The number of hours of daylight, H, on day d of any given year in Fairbanks, Alaska, can be modeled by H (d) = 12 + 8.3 sin (2π/365 (d − 80)). For the 80th day of the year, March 21st, determine the number of hours of sunlight Fairbanks had. Find the number of hours of sunlight in Fairbanks on the 355th day of the year, December 21st.
At a certain time of day, the angle of elevation of the Sun is 40∘. If the shadow of a tree is 35 ft long, determine the height of the tree.
A road has an incline of 6∘. After driving five thousand miles on this road, determine the increase in altitude for the driver. Round to the nearest foot.
A merry-go-round makes eight revolutions per minute. Find the linear speed, in feet per minute, of a horse ten feet from the center. Express the solution in terms of π and as a decimal round to the nearest tenth.
