Pre-Test on differential equations and an extra practice problem.

1. (1) The acceleration of a particle moving along the x-axis at any time t ≥ 0
is given by a(t) = 1 + e-t. At t = 0 the velocity of the particle is -2 and its
position is 3. The position of the particle at any time t is:
(A)
(B)
(C)
(D)
(E)

2. (2) Find the average rate of change of y with respect to x on the closed interval
[0, 3] if
(A)
(B)
(C)
(D)
(E)

3. (3) The curve that passes through the point (1, 0) and whose slope at any point
(x, y) is equal to has the equation
(A)
(B)
(C)
(D)
(E)

4. (4) If and y = 2 when , then y =
(A)
(B)
(C)
(D)
(E)

5. (1) The location of a slow-moving automobile in miles north of the Canada/USA
border on highway 75 is given by a function y = ƒ(t), where t represents time in
hours since noon yesterday. Suppose that ƒ(1) = 40, that is, the car is 40 miles
north of the border at 1:00 pm. The velocity of the car (in miles per hour) depends
on both time and location, and is given by the formula:
(a) Find the car’s velocity at t = 1.
(b) Determine an explicit formula for the location y = ƒ(t).
(c) Where is the car at 5:00 pm?

6. (1) The location of a slow-moving automobile in miles north of the Canada/USA
border on highway 75 is given by a function y = ƒ(t), where t represents time in
hours since noon yesterday. Suppose that ƒ(1) = 40, that is, the car is 40 miles
north of the border at 1:00 pm. The velocity of the car (in miles per hour) depends
on both time and location, and is given by the formula:
(b) Determine an explicit formula for the location y = ƒ(t).

7. (1) The location of a slow-moving automobile in miles north of the Canada/USA
border on highway 75 is given by a function y = ƒ(t), where t represents time in
hours since noon yesterday. Suppose that ƒ(1) = 40, that is, the car is 40 miles
north of the border at 1:00 pm. The velocity of the car (in miles per hour) depends
on both time and location, and is given by the formula:
(c) Where is the car at 5:00 pm?

8. A population of honeybees grows at an anuual rate equal to 1/4 the
number present when there are no more than 10,000 bees. If there are
more than 10,000 bees but fewer than 50,000 bees, the growth rate is
equal to 1/12 of the number present. If there are 5000 bees now, when
will there be 25,000 bees?