Questions from General Calculus

Q: The population of the world was about 6.1 billion in

The population of the world was about 6.1 billion in 2000. Birth rates around that time ranged from 35 to 40 million per year and death rates ranged from 15 to 20 million per year. Let’s assume that t...

Q: (a) Assume that the carrying capacity for the US population

(a) Assume that the carrying capacity for the US population is 800 million. Use it and the fact that the population was 282 million in 2000 to formulate a logistic model for the US population. (b) Det...

Q: One model for the spread of a rumor is that the rate

One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor...

Q: Biologists stocked a lake with 400 fish and estimated the carrying capacity

Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 10,000. The number of fish tripled in the first yea...

Q: (a) Show that if P satisfies the logistic equation (

(a) Show that if P satisfies the logistic equation (4), then (b) Deduce that a population grows fastest when it reaches half its carrying capacity.

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 7 depends on the initial value P0 and the proportionality constant k. Graph several members of this family. How...

Q: Find the radius of convergence and interval of convergence of the series

Find the radius of convergence and interval of convergence of the series.

Q: The table gives the midyear population of Japan, in thousands,

The table gives the midyear population of Japan, in thousands, from 1960 to 2010. Use a calculator to fit both an exponential function and a logistic function to these data. Graph the data points an...

Q: The table gives the midyear population of Norway, in thousands,

The table gives the midyear population of Norway, in thousands, from 1960 to 2010. Use a calculator to fit both an exponential function and a logistic function to these data. Graph the data points a...

Q: Let c be a positive number. A differential equation of the

Let c be a positive number. A differential equation of the form where k is a positive constant, is called a doomsday equation because the exponent in the expression ky11c is larger than the exponent 1...