Questions from General Calculus

Q: A bacteria culture grows with constant relative growth rate. The bacteria

A bacteria culture grows with constant relative growth rate. The bacteria count was 400 after 2 hours and 25,600 after 6 hours. (a). What is the relative growth rate? Express your answer as a percenta...

Q: Solve the differential equation. (y + sin y)

Solve the differential equation. (y + sin y) y' = x + x3

Q: Experiments show that if the chemical reaction N2O5 → 2NO2 + 1

Experiments show that if the chemical reaction N2O5 → 2NO2 + 1/2O2 takes place at 450C, the rate of reaction of dinitrogen pentoxide is proportional to its concentration as follows:...

Q: Strontium-90 has a half-life of 28 days.

Strontium-90 has a half-life of 28 days. (a). A sample has a mass of 50 mg initially. Find a formula for the mass remaining after days. (b). Find the mass remaining after 40 days. (c). How long does i...

Q: For which positive integers is the following series convergent? ∑∞n

For which positive integers is the following series convergent? ∑∞n=1 (n!)2/(kn)!

Q: The half-life of cesium-137 is 30 years.

The half-life of cesium-137 is 30 years. Suppose we have a 100-mg sample. (a). Find the mass that remains after years. (b). How much of the sample remains after 100 years? (c). After how long will onl...

Q: A population of protozoa develops with a constant relative growth rate of

A population of protozoa develops with a constant relative growth rate of 0.7944 per member per day. On day zero the population consists of two members. Find the population size after six days.

Q: A common inhabitant of human intestines is the bacterium Escherichia coli.

A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a cult...

Q: The Pacific halibut fishery has been modeled by the differential equation

The Pacific halibut fishery has been modeled by the differential equation where y (t) is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the...

Q: Suppose a population P (t) satisfies dP/dt =

Suppose a population P (t) satisfies dP/dt = 0.4P – 0.001P2, P (0) = 50 where t is measured in years. (a). What is the carrying capacity? (b). What is P'(0)? (c). When will the population reach 50% of...