Questions from Calculus

Q: Find a constant solution of y’ = t2y - 5t2.

Find a constant solution of y’ = t2y - 5t2.

Q: Let f (t) be the size of a paramecium population

Let f (t) be the size of a paramecium population after t days. Suppose that y = f (t) satisfies the differential equation y’ = .003y (500 - y), y (0) = 20. Describe this initial-value problem in wo...

Q: Let q = f (p) be the demand function for

Let q = f (p) be the demand function for a certain commodity, where q is the demand quantity and p the price of 1 unit. In Section 5.3, we defined the elasticity of demand as E( p) = -p f ‘( p) / f...

Q: Find the demand function if the elasticity of demand is a linear

Find the demand function if the elasticity of demand is a linear function of price given by E( p) = ap + b, where a and b are constants.

Q: When a red-hot steel rod is plunged in a bath

When a red-hot steel rod is plunged in a bath of water that is kept at a constant temperature 10˚C, the temperature of the rod at time t, f (t), satisfies the differential equation y = k[10 - y],...

Q: Rework Exercise 13 for a metal with a constant of proportionality k

Rework Exercise 13 for a metal with a constant of proportionality k = .2. Which rod cools faster, the rod with a constant of proportionality k = .1 or the rod with a constant of proportionality k = .2...

Q: A body was found in a room when the room’s temperature was

A body was found in a room when the room’s temperature was 70˚F. Let f (t) denote the temperature of the body t hours from the time of death. According to Newton’s law of cooling, f satisfies a differ...

Q: Derive the formula for the population in Example 3, if the

Derive the formula for the population in Example 3, if the population in 1995 was 2 million. (The formula is given following the solution of Example 3.) Example 3: In 2005, people in a country suffer...

Q: In an experiment, a certain type of bacteria was being added

In an experiment, a certain type of bacteria was being added to a culture at the rate of e0.03t + 2 thousand bacteria per hour. Suppose that the bacteria grow at a rate proportional to the size of the...

Q: Find a formula for P(t) in Exercise 17 if

Find a formula for P(t) in Exercise 17 if, initially, 10,000 bacteria were present in the culture. Exercise 17: In an experiment, a certain type of bacteria was being added to a culture at the rate o...