Questions from General Calculus

Q: (a). Make a guess as to the carrying capacity for

(a). Make a guess as to the carrying capacity for the US population. Use it and the fact that the population was 250 million in 1990 to formulate a logistic model for the US population. (b). Determine...

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 of the population who have heard the rumor and the fraction who have not heard the rumor....

Q: Populations of aphids and ladybugs are modeled by the equations

Populations of aphids and ladybugs are modeled by the equations (a). Find the equilibrium solutions and explain their significance. (b). Find an expression for dL/dA. (c). The direction field for th...

Q: In Example 1 we used Lotka-Volterra equations to model populations

In Example 1 we used Lotka-Volterra equations to model populations of rabbits and wolves. Let’s modify those equations as follows: (a). According to these equations, what happens t...

Q: Determine whether the series is convergent or divergent. If it is

Determine whether the series is convergent or divergent. If it is convergent, find its sum.

Q: In Exercise 10 we modeled populations of aphids and ladybugs with a

In Exercise 10 we modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows: (a). In the absence of ladybugs, what does the model predict...

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

The table gives the midyear population of Japan, in thousands, from 1960 to 2005. Use a graphing calculator to fit both an exponential function and a logistic function to these data. Graph the data...

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

The table gives the midyear population of Spain, in thousands, from 1955 to 2000. Use a graphing calculator to fit both an exponential function and a logistic function to these data. Graph the data...

Q: Let’s modify the logistic differential equation of Example 1 as follows:

Let’s modify the logistic differential equation of Example 1 as follows: (a). Suppose P (t) represents a fish population at time t, where is measured in weeks. Explain the meaning...

Q: Consider the differential equation as a model for a fish population,

Consider the differential equation as a model for a fish population, where is measured in weeks and c is a constant. (a). Use a CAS to draw direction fields for various values of c. (b). From your d...