Refer to page 74 for a non-homogeneous differential equation. Solve it using the method of variation of parameters. Outline each step clearly, including finding the complementary solution and particular solution. Instructions: Focus on solving the problem only. Provide a detailed step-by-step solution, show all calculations, and avoid irrelevant explanations. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]

UCLAium-1919 is a radioactive element with a half-life of 140 days. Suppose that 10 mg of the element are placed in a lead container. Let y(t) represent the number of mg present t days later. Give exact answers only for all parts. No decimals, no rounding. The equation that represents the number of mg present t days later is y(t) = How many mg will be present after 10 weeks? Answer = In how many days will it take for 70% of the original sample to decay? Answer =

Please answer with illustration and handwritten solution. A dirty lake was contaminated by a toxic substance. The lake has a volume of 100,000 liters of water with 9k lbs of the toxic substance.  To solve this problem, they intentionally pour 1,000 liters of pure clean water per hour and release the toxic water with the same rate.   a. find its differential equation. b. amount of toxic after a day.

Given an estimated regression equation, y = 39.1674 + 1.0161X1 – 1.8616X2, solve for the y if X1 = 1.19 and X2 = 11.60

Please Solve In 20mins

The third bacteria culture started with 5,000 bacteria. The assistant found that after 3 hours the estimated population was 80,000. 3. How long did it take for the population to double for the first time? How long after that (a) will it take for the population to double the second time? How long after that will it take for the population to double the third time? Find an equation that can be used to predict the size of the population at any time t. Estimate the population after 3.5 hours. (b) (c) How does the doubling time found in (a) relate to your equation in (b)? Find a general formula (or rule) that can be used to predict the bacteria population for any culture. You should define what each variable in your general formula stands for. You should illustrate how your general formula applies to each of the three scenarios in this investigation! 4.

The amount of radioactive contaminant evenly distributed in a reactor closed is measured by its concentration c (becquerel/liter or Bq/L). the contaminant it decreases at a rate of decay proportional to its concentration; that is, Decay rate = –kc where k is a constant, with unit of day–1 . Therefore, according to the Equation below, a mass balance for the reactor can be written as Use Euler's method to solve this equation from t=0 to 0.5d with k=0.175 d–1 . use a step size ∆t = 0.1 d. The concentration at t = 0 is 100 Bq/L.

The half-life of cesium-137 is 30 years. Suppose you have a 80 mg sample. After how long will only 1 mg remain?  Leave your answer in exact form. You must show all work to receive full credit.

A radioactive substance is decaying according to the formula y = Be-0.02t where y mg is the amount present t years from now. How long will it take for half the substance to decay? Round-off to the nearest integer.

In 1991 it was estimated that there were about 100 breeding pairs of Northern Spotted Owls. It was determined that their population had been declining at a rate of 7% each year. If 'P' is the population of the owls, write the equation that would model the population of the Northern Spotted Owl after t years. O A.P = 100 (93)* O B. P = 100 (7%)' OC.P= 100 (1.7)* OD. P = 100 (7)