Questions from Calculus

Q: Is the constant function f (t) = -4 a

Is the constant function f (t) = -4 a solution of the differential equation y’ = t2 (y + 4)?

Q: In certain learning situations a maximum amount, M, of information

In certain learning situations a maximum amount, M, of information can be learned, and at any time, the rate of learning is proportional to the amount yet to be learned. Let y = f (t) be the amount of...

Q: Mothballs tend to evaporate at a rate proportional to their surface area

Mothballs tend to evaporate at a rate proportional to their surface area. If V is the volume of a mothball, then its surface area is roughly a constant times V2/3. So the mothball’s volume decreases a...

Q: Some homeowner’s insurance policies include automatic inflation coverage based on the U

Some homeowner’s insurance policies include automatic inflation coverage based on the U.S. Commerce Department’s construction cost index (CCI). Each year, the property insurance coverage is increased...

Q: The Gompertz growth equation is dy/dt = -

The Gompertz growth equation is dy/dt = -ay ln y/b, where a and b are positive constants. This equation is used in biology to describe the growth of certain populations. Find the general form of sol...

Q: If the function f (t) is a solution of the

If the function f (t) is a solution of the initial-value problem y’ = 2y - 3, y(0) = 4, find f (0) and f ‘(0).

Q: When a certain liquid substance A is heated in a flask,

When a certain liquid substance A is heated in a flask, it decomposes into a substance B at such a rate (measured in units of A per hour) that at any time t is proportional to the square of the amount...

Q: Let f (t) denote the number (in thousands)

Let f (t) denote the number (in thousands) of fish in a lake after t years, and suppose that f (t) satisfies the differential equation y' = 0.1y (5 - y). The slope field for this equation is shown i...

Q: Refer to the differential equation in Exercise 39. (a

Refer to the differential equation in Exercise 39. (a) Obviously, if you start with zero fish, f (t) = 0 for all t. Confirm this on the slope field. Are there any other constant solutions? (b) Describ...

Q: Solve the following differential equations: dy/dt = -

Solve the following differential equations: dy/dt = -1/t2y2