ST 552

Calculus on a Computer

 

Assignment 11 – More on Anti-derivatives

 

For problems 1 – 3, sketch three possible anti-derivatives of the given functions.

 

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  1. Solve by separating variables:

 

  1.  Newton’s Law of Cooling states that the rate of change of the temperature of an object is proportional to the difference in temperatures of the object and the ambient temperature.  Write this as a differential equation.

 

  1. If my coffee starts at 180, and after 10 minutes is at 160, when will it hit 100?  Assume room temperature is 70.

 

  1. Suppose a population has a carrying capacity of K. This means that the growth rate is zero for P=K.  Suppose that the per capita growth rate is linear.  This gives
    1. Explain the differential equation.
    2. Solve.
    3. Let K = 1000, and let P(0)=100, then 500, then 1000, then 1200.  Sketch the solutions.
    4. Discuss.

 

  1. If P is the amount owed on a loan, r is the annual percentage rate, and M is the monthly payments, we get .
    1. Explain the given differential equation.
    2. Find the monthly payment to pay off a $50,000 loan in 30 years.
    3. In 15 years?