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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- Solve
by separating variables:
- 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.
- If my
coffee starts at 180, and after 10 minutes is at 160, when will it hit
100? Assume room temperature is 70.
- 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
- Explain
the differential equation.
- Solve.
- Let
K = 1000, and let P(0)=100, then 500, then 1000,
then 1200. Sketch the solutions.
- Discuss.
- If P
is the amount owed on a loan, r is the annual percentage rate, and M is
the monthly payments, we get .
- Explain
the given differential equation.
- Find
the monthly payment to pay off a $50,000 loan in 30 years.
- In 15
years?