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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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
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?
Consider a fish tank that initially contains 300 liters of water with 100 grams of salt dissolved in it. Water containing 4 grams of salt per liter is allowed to run into the tank at a rate of 2 liters per minute. The thoroughly stirred mixture in the tank is also allowed to drain out at a rate of 3 liters per minute. Find a differential equation for the amount of salt m(t) in the tank at time t. (You don’t need to solve the differential equation.)
Let f(t) be the balance in a savings account at the end of t years. Suppose that y = f(t) satisfies the differential equation y′ = .04y + 2000.(a) If after 1 year the balance is $10,000, is it increasing or decreasing at that time? At what rate is it increasing ordecreasing at that time?(b) Write the differential equation in the form y′ = k(y + M).(c) Describe this differential equation in words.
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
The population, y(t) (in thousands) of rabbits on an island has an intrinsic growth rate of 28% per year (ie that's the rate it would grow absent limiting factors). However the population has a carrying capacity (aka saturation level or maximum sustainable population) of 9 thousand rabbits. Additionally, in order to have sufficient genetic diversity, the population must stay above a threshold (aka minimum sustainable population) of 4 thousand rabbits. Write a differential equation for the population of rabbits. dy Preview dt ||

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