1. Under ideal conditions, a population of rats has an exponential growth rate of 13.6% per day. Consider an initial population of 100 rats.
a. Find the exponential growth function.
b. What will the population be after 7 days? After 2 weeks?
c. Find the doubling time.
2. Jack and Susan have just celebrated the birth of a daughter. They want to make a onetime deposit of money into an interest-bearing account so that their daughter will have $50,000 for college at age 18. At a rate of 3.5%, compounded continuously, how much money do they need to deposit?
3. Suzie owns a car and moped. She can afford 14 gallons of gasoline to be split between the car and the moped. Suzie's car gets 30 mpg and, with the fuel currently in the tank, can hold at most an additional 12 gallons of gas. Her moped gets 100 mpg and can hold at most 4 gallons of gas. How many gallons of gasoline should each vehicle use if Susie wants to travel as far as possible? What is the maximum number of miles that she can travel?
After solving your chosen problem, write a one to two (1-2) page paper providing a step-by-step explanation of how you solved the problem as if you were explaining it to another person. Your explanation should have the following elements, which should be used as headers in your paper:
1. Put the problem in context. (Use a header titled "Context".)
a. Identify the topics in this course the problem relates to.
2. Explain your choice of method of problem solving. (Use a header titled "Method".)
a. Explain the variety of ways to solve the problem.
b. Provide your rationale for selecting the method you adopted.
Write out a step-by-step explanation of how the problem is solved as if you were explaining it to another person. (Use a header titled "Explanation". )
Clearly state the solution. Solution is correct. (Use a header titled "Conclusion".)