Insects that are adapted to life in wet, tropical regions seem to prefer just the right...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Insects that are adapted to life in wet, tropical regions seem to prefer "just the right amount" of rainfall: In a recently concluded five-year study in northern Peru, Felicity Newell and coworkers found that short periods of both drought conditions and heavier-than-usual rainfall led to a 50% decline in arthropod (insect and spider) abundance. A function that captures the main features of the observed relationship between precipitation p (the 90-day rainfall measured in mm) and the arthropod biomass A (measured in mg/m²) is (a) Find the derivative A₁ (p) = A1 (p) = 60 - -A₁ (p). dp 2 (P-10⁰0) ². 60 For differentiation practice, calculate A₁ (p) using the following two approaches (you should of course verify that your answers agree...): i. Multiply out (expand the square) to write A₁ in the form of a general quadratic func- tion, A₁ (p) = ap²+bp+c; then differentiate using rules for derivatives of polynomials. ii. Write A1 (p) = 60 - (g(p))² where g(p) = P-400 and use the chain rule. 3 60 (Equivalently, A₁ (p) = 60 (fog) (p) = 60-f(g(p)) for f(u) = u², g(p) as above.) (b) In a rain forest that receives 500 mm of seasonal rainfall, what is the rate of change of biomass A₁ with respect to precipitation? (c) When (for which interval(s) of p values) does increasing precipitation increase biomass A₁ (p)? When does it decrease biomass? Now let us consider two other functions A2 and A3 that look qualitatively similar to A₁, as seen in the figure to the right. [The chain rule (and for A3, also the quotient rule) will be necessary to find the derivatives of these func- tions...] Find the derivative A₂ (p). g/m²) A2 (p) = 60 - 2 arthropod biomass A 60 20 0 100 functions A1, A2 and A3, shifted to show differences 200 300 400 500 precipitation p (mm) 600 (d) An alternative model for the dependence of biomass on precipitation is given by P-4008/5 60 700 A_1(p) A_2(p) A_3(p) 800 (e) Another possible function relating precipitation and biomass is Find the derivative A3 (p). A3 (p) = 60-6- P-400 60 2 2 √√10+ (2,00) ² P-400 60 Insects that are adapted to life in wet, tropical regions seem to prefer "just the right amount" of rainfall: In a recently concluded five-year study in northern Peru, Felicity Newell and coworkers found that short periods of both drought conditions and heavier-than-usual rainfall led to a 50% decline in arthropod (insect and spider) abundance. A function that captures the main features of the observed relationship between precipitation p (the 90-day rainfall measured in mm) and the arthropod biomass A (measured in mg/m²) is (a) Find the derivative A₁ (p) = A1 (p) = 60 - -A₁ (p). dp 2 (P-10⁰0) ². 60 For differentiation practice, calculate A₁ (p) using the following two approaches (you should of course verify that your answers agree...): i. Multiply out (expand the square) to write A₁ in the form of a general quadratic func- tion, A₁ (p) = ap²+bp+c; then differentiate using rules for derivatives of polynomials. ii. Write A1 (p) = 60 - (g(p))² where g(p) = P-400 and use the chain rule. 3 60 (Equivalently, A₁ (p) = 60 (fog) (p) = 60-f(g(p)) for f(u) = u², g(p) as above.) (b) In a rain forest that receives 500 mm of seasonal rainfall, what is the rate of change of biomass A₁ with respect to precipitation? (c) When (for which interval(s) of p values) does increasing precipitation increase biomass A₁ (p)? When does it decrease biomass? Now let us consider two other functions A2 and A3 that look qualitatively similar to A₁, as seen in the figure to the right. [The chain rule (and for A3, also the quotient rule) will be necessary to find the derivatives of these func- tions...] Find the derivative A₂ (p). g/m²) A2 (p) = 60 - 2 arthropod biomass A 60 20 0 100 functions A1, A2 and A3, shifted to show differences 200 300 400 500 precipitation p (mm) 600 (d) An alternative model for the dependence of biomass on precipitation is given by P-4008/5 60 700 A_1(p) A_2(p) A_3(p) 800 (e) Another possible function relating precipitation and biomass is Find the derivative A3 (p). A3 (p) = 60-6- P-400 60 2 2 √√10+ (2,00) ² P-400 60
Expert Answer:
Related Book For
Intermediate accounting
ISBN: 978-0077647094
7th edition
Authors: J. David Spiceland, James Sepe, Mark Nelson
Posted Date:
Students also viewed these accounting questions
-
Assume the density of water as 1000/3 and = 9.81/ 2 An oil tank with vertical sides is 3 wide and contains oil with a density of 800/3 to a depth of 1.8. Calculate the hydrostatic thrust on the side...
-
Rainfall In a well-known study on the effects of cloud seeding to produce rainfall, experimenters randomly assigned air planes to release either silver nitrate (which is believed to increase the...
-
Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...
-
M DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO SECTION B. ANSWER ANY THREE (3) QUESTIONS Question 1 (25 marks) You have analyzed Solar Power Ltd. and have reported the results of your analysis...
-
Google is a company that embraces innovation. What are some actions Google takes to ensure they are creating an environment that supports innovation?
-
Richard Harding is the sheriff of Howard County, Indiana. In addition to the usual law enforcement duties, the sheriff has the responsibility of maintaining the detention facility (i.e., county...
-
On January 2, 2015, Winstead & Company purchased 1,000,000 shares of the Secrest Company for \($32\) million. The investment represented 40 percent of the outstanding common shares of The Secrest...
-
Cunningham Company reports a retained earnings balance of $365,200 at the beginning of 2007. For the year ended December 31, 2007, the company reports pretax income from continuing operations of...
-
You are considering opening a new plant. The plant will cost $100 million up front and will take one year to build. After that, it is expected to produce profits of $30 million at the end of the year...
-
Angus Walker, CFA, is reviewing the defined benefit pension plan of Acme Industries. Based in London, Acme has operations in North America, Japan, and several European countries. Next month, the...
-
During 20X1, Discolux Ltd. had two classes of shares outstanding: . Class A preferred shares, 3,000 shares issued and outstanding at the beginning of the year; quarterly dividend rate of $250 per...
-
Procter and Gamble (PG) paid an annual dividend of $2.95 in 2021 . You expect PG to increase its dividends by 8.3 % per year for the next five years (through 2026), and thereafter by 3.5% per year....
-
1.You are considering an investment that will pay $17846 in 20 years. If the interest rate is 14.88%, what is the most you should be willing to invest today? (Round to 2 decimal places.) 2.A company...
-
As an electrical engineering apprentice working in the maintenance department of your company. Your employer is looking to introduce a wind generator mounted to the roof of the factory to reduce...
-
For this question: To deal with these and other concerns, Patria's Parliament changed Patria's tax code to impose a "luxury tax" of 10 percent ad valorem on all products sold in Patria, be they...
-
Suppose that you borrow $17,000 for a new car. You can select one of the following loans, each requiring regular monthly payments: Installment Loan A: three-year loan at 5.7% Installment Loan B:...
-
Write a real Fortran function Series(x) which returns an approximate sum of the sequence I 1! - 23 + - 2! 3! 4! + i.e., which adds consecutive elements of this sequence until the addition of another...
-
The landing gear of an aircraft with: mass of 2000 kg the spring-mass-damper system Consider that the runway surface is y(t) = 0.2 cos 157.08t stiffness of the spring is 5 x 105 N/m. What is the...
-
On January 1, 2013, the Montgomery Company agreed to purchase a building by making six payments. The first three are to be $25,000 each, and will be paid on December 31, 2013, 2014, and 2015. The...
-
The comparative balance sheets for 2013 and 2012 are given below for Surmise Company. Net income for 2013 was $50 million. Required: Prepare the statement of cash flows of Surmise Company for the...
-
During 2013, its first year of operations, Baginski Steel Corporation reported an operating loss of $375,000 for financial reporting and tax purposes. The enacted tax rate is 40%. Required: 1....
-
Using Rules 5.1, show that if \(x>0\) and \(y <0\) then \(x y <0\), and that if \(a>b>0\) then \(\frac{1}{a}
-
For which values of \(x\) is \(x^{2}+x+1 \geq \frac{x-1}{2 x-1}\) ?
-
For which values of \(x\) is \(-3 x^{2}+4 x>1\) ?
Study smarter with the SolutionInn App