Question

A khanacademy.org Differential equations: exponential model word problems You might need: Calculator A controversial story comes out in the school newspaper. The number of students who have not heard about the story decreases at a rate that is proportional at any time to the number of students who have not heard the story at that time. There were 900 students who had not heard the story initially, and the number of students is divided by 3 every 4 days. How many students have not heard the story after 7 days? Round to the nearest student. students Stuck?

Answer 1

132 students

Explanation:

Let S(t) model the number of students who have not heard the story after t days.

We are told that the rate of change of S is proportional to S:

`(dS)/(dt) = kS`

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This sort of differential equation describes an exponential model, and its solution is

`S(t) = C` *
`e^(kt)`

Let's find the values for C and k.

We are told that there were 900 students who had not heard the story initially. From this we can tell that C=900

We are also told that the number of students is divided by 3 every4 days. From this we can tell that
`k= (ln(0.3))/(4)`

We found that
`S(t) = 900e^{(ln(0.3))/(4)t }`, The number of students who have not heard the story after 7 days is S(7):

`S(7) = 900e^{(ln(0.3))/(4)(7) }` ≈ 132