Questions from General Calculus

Q: Suppose you have just poured a cup of freshly brewed coffee with

Suppose you have just poured a cup of freshly brewed coffee with temperature 950C in a room where the temperature is 200C. (a). When do you think the coffee cools most quickly? What happens to the rat...

Q: Suppose that a population develops according to the logistic equation dP/

Suppose that a population develops according to the logistic equation dP/dt = 0.05P – 0.0005P2 where t is measured in weeks. (a). What is the carrying capacity? What is the value of...

Q: Suppose that a population grows according to a logistic model with carrying

Suppose that a population grows according to a logistic model with carrying capacity 6000 and k = 0.0015 per year. (a). Write the logistic differential equation for these data. (b). Draw a direction f...

Q: The table gives estimates of the world population, in millions,

The table gives estimates of the world population, in millions, from 1750 to 2000. (a). Use the exponential model and the population figures for 1750 and 1800 to predict the world population in 1900...

Q: The table gives the number of yeast cells in a new labora

The table gives the number of yeast cells in a new labora tory culture. (a). Plot the data and use the plot to estimate the carrying capacity for the yeast population. (b). Use the data to estimate...

Q: Sketch a direction field for the differential equation. Then use it

Sketch a direction field for the differential equation. Then use it to sketch three solution curves. y' = x – y + 1

Q: Explain why the functions with the given graphs can’t be solutions of

Explain why the functions with the given graphs can’t be solutions of the differential equation

Q: Suppose that the radius of convergence of the power series ∑cnxn

Suppose that the radius of convergence of the power series ∑cnxn is R. What is the radius of convergence of the power series ∑cnx2n?

Q: For a fixed value of M (say M = 10),

For a fixed value of M (say M = 10), the family of logistic functions given by Equation 4 depends on the initial value P0 and the proportionality constant k. Graph several members of this family. How...

Q: A glucose solution is administered intravenously into the bloodstream at a constant

A glucose solution is administered intravenously into the bloodstream at a constant rate r. As the glucose is added, it is converted into other substances and removed from the bloodstream at a rate th...