Stewart_Calc_7ET ch09sec01
MULTIPLE CHOICE
1. Which equation does the function satisfy?
a.
b.
c.
d.
e.
2. A population is modeled by the differential equation.
For what values of P is the population increasing?
a.
b.
c.
d.
e.
3. Solve the initial-value problem.
a.
b.
c.
d.
e.
4. Newton’s Law of Cooling states that the rate of cooling of an object is proportional to the
temperature difference between the object and its surroundings. Suppose that a roast turkey
is taken from an oven when its temperature has reached and is placed on a table in a
room where the temperature is . If is the temperature of the turkey after t minutes,
then Newton’s Law of Cooling implies that
.
This could be solved as a separable differential equation. Another method is to make the
change of variable . If the temperature of the turkey is after half an hour,
what is the temperature after 35 min?
a.
b.
c.
d.
e.
MULTIPLE RESPONSE
1. For what values of k does the function satisfy the differential equation
?
a.
b.
c.
d.
e.
2. For what nonzero values of k does the function satisfy the differential
equation for all values of A and B?
a.
b.
c.
d.
e.
3. Which of the following functions are the constant solutions of the equation
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. is the solution of the differential equation . Find the solution that satisfies
the initial condition .
2. A population is modeled by the differential equation
.
For what values of P is the population decreasing?
3. A function satisfies the differential equation .
What are the constant solutions of the equation?
4. A sum of is invested at interest. If is the amount of the investment at time
t for the case of continuous compounding, write a differential equation and an initial
condition satisfied by .