Question

In: Advanced Math

1.) use partial fractions to decompose each into a fraction with a linear factor in the...

1.) use partial fractions to decompose each into a fraction with a linear factor in the denominator:

a.) 2/(x+1)(x+2)

b.) 2/(y)(100-y)

c.) y/(y)(100-y)

d.) 5/x(x+1)(x-2)

e.) 2x+3/x(x+1)(x-2)

f.) x^2/x(x+1)(x-2)

2. Consider the ODE model for population growth:

a. Use separation of variables to determine the solution.

b. What is the value of y(1)?

c. What is the value of y(10)?

d. At what time will the population reach 100? At what time will it reach 1000?

3. Consider the logistic growth model for population growth:

a. Use separation of variables to determine the solution.

b. What is the value of y(1)? c. What is the value of y(10)?

d. At what time will the population reach 100? At what time will it reach 1000?

4. Consider the solutions to the previous two problems

a. What does the first model predict about solutions as t increases?

b. What does the second model predict about solutions as t goes to infinity?

c. Use MATLAB’s ODE45 command to generate plots of the solutions, give a plot of the two functions together on a single set of axes.

d. How are values similar or different for this model in comparison to the previous one?

Expert Solution

Colby Messinger answered 2 days ago

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