3) A polluted river has an initial concentration of a heavy metals of 10 parts/m3. Theconcentration of the heavy metals will reduce as rain falls into the rain. The concentration C ofthe pollutant as a function of time (in weeks) is given bydC+ 0.056C = 0, C(0) = 107dtUsing Heun's method and a step size of 3.5 weeks, find the concentration of the pollutant at 7weeks.

Given: dCdt+0.056C=0 C0=107 Step size h=3.5 To find: Find the concentration of the pollutant at 7…

Answered: A polluted river has an initial…

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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Newton's Law of Cooling tells us that the rate of change of the temperature of an object is proportional to the temperature difference between the object and its surroundings. This can be modeled by the differential equation =k(TA), where T is the temperature of the object after t units of time have passed, A is dT dt the ambient temperature of the object's surroundings, and k is a constant of proportionality. Suppose that a cup of coffee begins at 179 degrees and, after sitting in room temperature of 62 degrees for 14 minutes, the coffee reaches 170 degrees. How long will it take before the coffee reaches 160 degrees? Include at least 2 decimal places in your answer. minutes
The half-life of krypton-91 (91Kr) is 10 s. At time t = 0 a heavy canister contains 4 g of this radioactive gas. (a) Find a function m(t) = mo2-t/h that models the amount of 91Kr remaining in the canister after t seconds. m(t) = (b) Find a function m(t) = moe-rt that models the amount of 91Kr remaining in the canister after t seconds. (Round your r value to five decimal places.) m(t) = (c) How much 91Kr remains after 1 min? (Round your answer to three decimal places.) 10 (d) After how long will the amount of 91Kr remaining be reduced to 1 ug (1 microgram, or 10-6 g)? (Round your answer to the nearest whole number.) wmnod sec R S D G V B alt in control option comimand Command
A endangered species is released into a park. The population of an endangered species is expected to follow the logistic model p(t)= 810/1+8e-188t . Where t is measured in mionths. a. How many endangered species were released into the park? b. How many endangered species will there be in 5 months? c. As time goes by, what appears to be the maximum population in the park?
A tree farm starts with ten trees. Tree growth is expected to follow logistic growth with a first-order growth rate constant of r = 0.16 yr ' to a maximum of 8,000 trees. Write the equation that relates the number of trees (N) to time (1). What are the values of No, r, and K? Plot the number of trees over time if no harvesting occurs. Go out to about 70 years. What is the maximum sustainable yield (MSY)? How long should you wait before harvesting at the MSY? Determine the standing crop. (The standing crop is the number of trees at steady state when harvesting at the MSY.)
Tank A initially contains 500 Litres of a brine solution with a concentration of 0.5 kg perlitre and tank B contains 500 Litres of water. Solution is pumped from tank A to tank B ata rate of 4 Litres /min and from tank B to tank A at a rate of 8 Litres /min. The tanks are keptwell stirred. Let the number of kilograms of salt in tank A be A1 after t minutes and B1in tank B.(a) Write down equations showing, respectively, the concentrations C1 and C2 inthe tanks after t minutes.(b) Write down two differential equations to show how A1 and B1 vary with time.(c) What is the relation between A1 and B1?(d) Eliminate B1 between the two equations in (b) and solve the resulting equationfor A1.(e) What is the concentration in tank A after 10 minutes?
PLZ HELP WITH THIS PROBLEM. Suppose a bacteria in a culture is growing at a rate of r(t)=10sint+6 measured in thousand bacterium per minute. By how much has the population of the bacteria increased from 0 minutes to 2pi minutes?

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