The balance sheet reports a.net income. b.expenses. c.revenue. d.liabilities.'

Assuming P≥0, suppose that a population develops according to the logistic equation ????P/????????=0.07P−0.00014P2 where ???? is

Natasha2012 [34]

Answer:

A complete description of the problem and solutions to each point are given below.

Explanation:

The Logistic Growth model of a population is defined as follows:

dP/dt = kP (1 - P/M) (1)

Where:

dP/dt is the population growth rate.

k is the maximal individual growth rate for a given population

P is the number of individual in the population

M= carrying capacity of the population.

In the problem this first order derivative ecuation is given by

dP/dt= 0,07P - 0,00014P² (2)

So, we can factorize ecuation (1) and compare it with (2) to find the carryng capacity and k value (questions 1 and 2).

kP (1 - P/M) = 0,07P - 0,00014P²

kP - (k/M)P² = 0,07P - 0,00014P²

Here kP = 0,07P ⇒ k = 0,07 (answer to question 2)

Then, (k/M)P² = 0,00014P²⇒ (k/M) = 0,00014 and given that k= 0,07

⇒ 0,07/M = 0,00014 ⇒ M = 0,07/0,00014 ⇒ M=500 (answer to question 1)

Finally to find for which values of P is the population increasing/decreasing, we have to find the values at which dP/dt is zero. Analyzing the equation as a quadratic function (applying Baskara´s equation) we find that the values at which dP/dt is zero are P= 0 and P = -1.

x = [-0,07 ± √(0,07²)]/ 0,14 ⇒ x= [-0,07 ± 0,07)]/ 0,14 ⇒ x = 0 and x= -1.

Then the vertex here is P = -0,5.

Now we can state that for P greater than - 0,5 the population is decreasimg (question 4), while for values from -∞ to - 0,5 the population is increasing (question 3).

Summarizing, given the first order derivative, the carrying capacity of the population is 500, the value of k is 0,07, the values of P for which dP/dt is positive (incresing population) are those comprised in the range (-∞, -0,5) and those for which the population is decreasing are (-0,5,∞).

3 0

3 years ago

You have recently opened your own internet website design business. You charge your clients $500 per project and are considering

faltersainse [42]

Answer:

hmm good question im not sure

Explanation:

7 0

3 years ago

small accounting firm is considering the purchase of a computer software package that would greatly reduce the amount of time ne

galina1969 [7]

Answer:

Pay back period =3 years 4 months

Explanation:

The payback period is the estimated length of time it takes cash inflow from a project to recoup the cash outflow.

The payback period uses cash flows and not profit.

The payback period can be determined by accumulation the cash inflow consecutively to ascertain the length of time it will take the sum to equate the initial cost.

This will be done as follows:

The sum of the cash in flows for the first three years would equal

650× 3= 1,950

The balance required to equate 2,150 would be

balance = 2150-1950 = 200

Pay back period = 3 years + (200/650)× 12 months

= 3 years 3.6months

Pay back period =3 years 4 months

7 0

3 years ago

Why was the national banking system developed?

Brilliant_brown [7]

This was developed for the fact to have a common bank across the nation. This is for the purpose of a national currency and to get rid of the financial crisis

3 0

3 years ago

Suppose two firms have identical sales, operating costs, employee competence, assets, and financing policies. These firms would

Feliz [49]

Answer:

False.

Explanation:

Profit can be defined as the financial benefit received by a business organization when the total revenue exceeds the total costs. Revenues are as result of the sales while the total costs include; costs of running the business, expenditures and taxes. Profit can be calculated using the formula below;

P=R-C

where;

P=profits

R=total revenue

C=total costs

This can also be expressed as;

Profits=Total revenue-total costs.

In the case above, even if the two firms have identical sales, operating costs, employee competence, assets, and financing policies, they don't have identical tax liability. Tax liability can be defined as the amount of tax that is owed to an authority usually the government. Firms usually differ in the amount of tax they are to pay with regard to numerous factors. One factor is that whether the firm is registered as an S corporation or not. An S corporation is a company that does not pay corporate tax. The taxes in an S corporation are filed on individual incomes thus avoiding double taxation.

3 0

4 years ago