NO WIKI or PLAGIARIZING!!

Reflect on the concepts of linear and non-linear systems. What concepts (only the names) did you need to accommodate the concept of linear and non-linear systems in your mind? What are the simplest linear system and non-linear system you can imagine? In your day to day, is there any occurring fact that can be interpreted as linear systems and non-linear systems? What strategy are you using to get the graph of linear systems and non-linear systems?

The world population in 1999 was approximately P₀ = 6.067 billion people, and in 2000, it was approximately P₁ = 6.145 billion people.

Logistic Growth Model. Scientists often use a different function to model population growth when there are limited resources, as is the case with our planet. To do this, we will model the world population (in billions of people) in year t by the function L(t) = P0K / P₀ + (K − P₀)e^-rbt , where P₀ and t are the same as above, r_b is a number called the base growth rate, and K is a number called the carrying capacity of the environment. Scientists estimate that the carrying capacity of the Earth is K = 15. Based on that, and the population data given above, you can calculate that r_b is about 0.022.

(a) Write down the function L(t) explicitly.

(b) Graph L(t) on the same axes as your function P(t) from Problem 1.

(c) According to this model, what would the population be in 2019? In 2049? In 2099?

(d) According to this model, how fast (in billions of people per year) is the world population growing in 2019? In 2049?

Suppose there is a corporate bond. Its face value is $2000. And the maturity is 4 years. Its coupon is $10 issued at the end of each year. Its price is $1900 right now. The interest rates for bonds and stocks are 2% and 3%, respectively. The market price of stock of this company is $25 right now. And the shares outstanding is 25,000 shares. And the tax rate is 20%. The ratio of debt to equity is 0.2.

1. Suppose the firm is going to repurchase some stocks now. It repurchased 5000 shares from the market at the current price. What is the stock price after the repurchase?
2. Suppose the firm is going to split its stock. It is a 2-to-1 split. (a share becomes two.) It requires commission of $ 2000. What is the stock price afterwards?
3. Suppose the firm issued cash dividend of $2 per share. What is the price afterwards?

In African cichlid fish, there are > 2000 different species that vary in their craniofacial structure based on whether they are pelagic (live in open water, feeding on smaller fish) or benthic (living at the bottom of the lake, feeding mostly on invertebrates such as snails). They are all derived from a common ancestor that may have left the Nile River and invaded at least three lakes including Lake Victoria, Lake Malawi, and Lake Tanganyika.

Describe how cichlids represent a relationship between the fields of developmental biology and evolution. Then describe another example of this relationship based on your textbook or a different resource. Limit your response to ten sentences. 8 pts

The key point of the case is : 6000 traditional bank jobs to go and 2000 new digital position created as NAB aims to move 60 percent of its business online over three years. redundancies are expected to cost up to $800 million. despite record underlying cash profit of $6.6bn, shares fall on cost blow out. Question? Using legitimacy theory,explain how your chosen theory applies to the NAB case, and what each group should do as a result of following the theory.(Make sure you relate your discussion to the NAB case and each of the affected groups under your chosen theory). Compare and contrast this theory and stakeholder theory and identify which of these theories is most important from the banks perspective and explain reasons why you think your chosentheory is the most important.

7. An investment has a cost of $2000. The investment will have a payout of X at the end of the first year. This initial payout X will grow at the rate of 10% per year for the next 3 years, then by 6% per year for the next 2 years, and then at the rate of 4% per year for the following 1 year. You believe the riskiness of this investment is 9%.

a. Calculate the smallest X that would entice you to invest.

1.The population of India in the year 2000 was 1 billion and it increased exponentially at a rate of 1.6% per year. If the growth rate is maintained, what will be the population in the year 2020? If the growth rate is decreased to 1.2% per year from 2020 onwards and is maintained at that level, what will be the population in the year 2050? Assuming the average human exhales 2.3 pounds of carbon dioxide on an average day, what is the total amount of Carbon released in the atmosphere annually by human exhalation (in billion tonnes) around the year 2020?  

2.Calculate the suspended particulate concentration (in μg/m³) in a sample collected through a hi-vol. sampler: Weight of clean filter = 5.00 g, Weight of the filter after exposure for 24 hours = 5.38 g, Average air flow = 2000 m³ in 24 hours.   

7. A genetic disorder occurs with probability 1/2000 . There is a test for this genetic disorder. If you have the disorder, then you test positive 90% of the time. If you don’t have the disorder, then you test negative 90% of the time.

If you test positive, what is the probability that you have the disorder?