Let P(t) be the population (in millions) of a certain city t years after 2015, and suppose that P(t) satisfies the differential equation P'(t)=0.03P(1), P(0)=2.(a) Use the differential equation to determine how fast the population is growing when it reaches 4 million people.(b) Use the differential equation to determine the population size when it is growing at a rate of 900,000 people per(c) Find a formula for P(1).year.OCCES

We have to find the correct Process to find how fast the population is growing , when it reaches 4…

Answered: Let P(t) be the population (in…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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dP dt =rP-ap² Think of a small population of fish growing in a public pond - P measures the number of fish and t measures the number of years since the pond was stocked. P' = 2P 0.01P² to allow harvesting of 75 fish per year, adapt the logistic model to handle this. That is, write a differential equation based on the logistic model that incorporates the idea of harvesting 75 fish per year. [Hint: (total rate) = (rate in) - (rate out) ]
A fish hatchery has 500 fish at time ? = 0. Each year 40 fish are harvested (evenly, throughoutthe year). The population’s instantaneous growth rate is 10% per year. Thus after 1 year, if nofish were harvested, there would be slightly more than 550 fish. a) Create the modeling differential equation for the amount of the number of fish in the hatchery, y, at time t.b) Solve the differential equation.c) Is there a steady-state level of the number of fish in the hatchery?
Let P(t) be the population (in millions) of a certain city t years after 2015, and suppose that P(t) satisfies the differential equation P'(t) = 0.04P(t), P(0) = 7. (a) Use the differential equation to determine how fast the population is growing when it reaches 10 million people. (b) Use the differential equation to determine the population size when it is growing at a rate of 600,000 people per year. (c) Find a formula for P(t). (a) Choose the correct process to find how fast the population is growing when it reaches 10 million people. A. Evaluate P'(t) = 0.04(10). B. Evaluate P'(t) = 0.04P(10). C. Solve 10 =0.04P(t) for P(t). D. Solve P'(10) = 0.04P(t) for P(t).
Let P(t) be the population (in millions) of a certain city t years after 2015, and suppose that P(t) satisfies the differential equation P'(t) = 0.02P(t), P(0) = 3. (a) Use the differential equation to determine how fast the population is growing when it reaches 6 million people. (b) Use the differential equation to determine the population size when it is growing at a rate of 800,000 people per year. (c) Find a formula for P(t). (a) Choose the correct process to find how fast the population is growing when it reaches 6 million people. A. Evaluate P'(t) = 0.02(6). B. Evaluate P'(t) = 0.02P(6). %3D C. Solve 6 = 0.02P(t) for P(t). D. Solve P'(6) = 0.02P(t) for P(t). %3D
(6) A bacterial culture contains y(0) grown to y(2) = 250[cells]. Construct and solve the differential equation assuming exponential growth. Determine the number of cells y(t) as a function of time. After how many hours does the bacterial culture 50[cells] at t O[hr]. After t = 2[hr], the bacterial culture has contain 2000 cells?
A virus has already infected 4 million people in a country before a vaccine becomes available to the public. Once vaccination starts, the number of infected people decreases at a rate that is proportional to the cube of the number of infected people. One month later, there are still 2 million people that are infected. Let p be the number of infected people (in millions) and t be the number of months since vaccination has started. (a) Find a differential equation and initial conditions to model the situation. (b) Solve the differential equation to find pp as a function of t (c) How many people are still infected three months after vaccination starts?
A 200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. A salt solution with 1/5 pound of salt per gallon is added to the tank at 10 gal/min, and the resulting mixture is drained out at 5 gal/min. Let Q(t) denote the quantity (lbs) of salt at time t (min). (a) Write a differential equation for Q(t) which is valid up until the point at which the tank overflows. 50t+ Q' (t) = X Check your variables you might be using an incorrect one. 50+t (b) Find the quantity of salt in the tank as it's about to overflow. 38.5 X Oll ✓ @ W # 3 e t² + c C $ 4 % 5 + 6 & 7 O * 8 O 9 11 OF
As a salt dissolves in methanol, the number x(t) of grams of the salt in a solution after t seconds satisfies the dx differential equation =1.6x-0.004x² (a) What is the maximum amount of the salt that will ever dissolve in the methanol? (b) If x=50 when t=0, how long will it take for an additional 50 g of salt to dissolve? (a) The maximum amount of the salt that will ever dissolve in the methanol is gijams. (Simplify your answer.) 5 AI 9 IN F5 F6 2 8 # B - U dt F7 → = ∞ A View an example Get more help. ↓ F8 H i 8 ↑ 2 e B F9 ↑ T' l Y F10 + + 1 8 *** F11 √i co Less F12 ● S Vi 2 Ө ÷ 1, A = Clear all L PRISC INS X U SCRLK - O HOME C V € Σ PAUSE PG UP 8 FR v -W. Check answer NUM (88) A S i x

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