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# At the start of a new movie at a theater there are 250 people in it. However, $10\%$ of the people walkout of the theater within15 minutes of the movie starting. If another $10\%$ leave in the 15 minutes and this rate continues for the duration of the movie, which of the following graphs appropriately models the number of people in the theater during the movie?

Last updated date: 20th Jun 2024
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Hint: This is a very interesting real life application of compounded interest value. Here we can see that one graph is a straight line, but the other three are the exponential curves. So, we have to make an equation by which we can find the relationship between time and number of people leaving the theater gradually. By using the suitable formula of compound interest with negative value of interest, we can find the solution.

Since, $10\%$ of the people walk out of the theater within the first $15$ minutes of the movie starting. Then, in the next 15 minutes $10\%$ of the remaining people are leaving the theater. This process goes on.
$A = P{\left( {1 - \dfrac{{10}}{n}} \right)^{nt}}$