(1)
Solve each IVP.
a.
z = 0.03z, z(0) = 4000
b.
(2)
Ra226 is a radioactive substance. From a sample of 20 g, 13 g remain after 1000 years.
a.
Determine the half-life of Ra226.
b.
(3)
y = –0.05(y – 72), y(0) = 183
Determine how much of this sample of Ra226 will be left after 1400 years.
A population grows exponentially at a continuous rate of 3% per day.
a.
Express this situation as a differential equation.
b.
If the population is 2000 after 5 days, find the initial population.
(4)
In Newton’s Law of (Anti-) Cooling, if ice cream is removed from the freezer, will the value
of k in the differential equation be positive or negative? Why? (Think carefully about this.)
(5)
Coffee is cooling in a Styrofoam cup. The proportionality constant k for this cup is –0.06.
The initial temperature of the coffee is 190° F, and the room temperature is 65°F.
a.
Write the IVP that represents this situation.
b.
(6)
Determine the coffee’s temperature (to the nearest tenth of a degree) after 30 minutes.
Coffee is cooling in a ceramic cup. The initial temperature of this coffee is 187° F, and the
room temperature is 68°F. After 10 minutes, the temperature of the coffee is 117° F. How
long (to the nearest tenth of a minute) will the coffee’s temperature stay above 90° F?
(7)
Sketch solution curves with the following initial points. Be sure to label each solution:
A(0, 3)
y


B(–2, –1)


x












(8)
Solve each IVP.
y  4 y; y(0)  3, y (0)  2
a.
b.
y  5 y; y(0)  0, y (0)  4
c.
y 
1
; y (9)  9
2y






C(3, 1)