Questions from General Calculus

Q: Let P(t) be the population (in millions)

Let P(t) be the population (in millions) of a certain city t years after 2015, and suppose that P(t) satisfies the differential equation P(t) = .03P(t), P(0) = 4. (a) Use the differential equation to...

Q: Approximately 10,000 bacteria are placed in a culture. Let

Approximately 10,000 bacteria are placed in a culture. Let P(t) be the number of bacteria present in the culture after t hours, and suppose that P(t) satisfies the differential equation P(t) = .55P(t...

Q: After t hours there are P(t) cells present in

After t hours there are P(t) cells present in a culture, where P(t) = 5000e0.2t. (a) How many cells were present initially? (b) Give a differential equation satisfied by P(t). (c) When will the initia...

Q: The size of a certain insect population is given by P(

The size of a certain insect population is given by P(t) = 300e0.01t, where t is measured in days. (a) How many insects were present initially? (b) Give a differential equation satisfied by P(t). (c)...

Q: Determine the growth constant of a population that is growing at a

Determine the growth constant of a population that is growing at a rate proportional to its size, where the population doubles in size every 40 days and time is measured in days.

Q: Determine the growth constant of a population that is growing at a

Determine the growth constant of a population that is growing at a rate proportional to its size, where the population triples in size every 10 years and time is measured in years.

Q: A population is growing exponentially with growth constant .05. In

A population is growing exponentially with growth constant .05. In how many years will the current population triple?

Q: Determine the growth constant k, then find all solutions of the

Determine the growth constant k, then find all solutions of the given differential equation. y' = 1.7y

Q: By trial and error, find a number of the form b

By trial and error, find a number of the form b = 2.(just one decimal place) with the property that the slope of the graph of y = bx at x = 0 is as close to 1 as possible.

Q: A person is given an injection of 300 milligrams of penicillin at

A person is given an injection of 300 milligrams of penicillin at time t = 0. Let f (t) be the amount (in milligrams) of penicillin present in the person’s bloodstream t hours after the injection. The...