Write first order linear differential equations that express the following situa

Question

Write first order linear differential equations that express the following situations. Let A be the amount of alcohol in someone's bloodstream at time t. The absorption of alcohol in the body is proportional to the amount remaining in the bloodstream at time t. Write a differential equation for the change in the amount of alcohol with time. Let A be the amount of radioactive carbon in a fossilized bone. The decay of radioactive carbon in the bone is proportional to the amount present at time t. Write a differential equation for the change in the amount of radioactive carbon with time. The increase in the number of people who have heard a rumor in a town of population P is proportional to the product of the number of people who have heard the rumor and the number who have not heard the rumor at time t. Write a differential equation for the change in the number of people who heard the rumor with time. A student in an engineering course finds the rate of increase of his grade

Explanation / Answer

a)

dA / dt = - a*A {A is amount of alcohol in blood at time t.}

b) - d A /dt = b*A    {q is amount of radioactive carbon in fossil fuels.}

c) dN/dt = c *N *(P-N) {N is number who know the rumour,P is population}

d) dG/dt =d * N / A { N is sudy hours ,A is spent online games}

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