Question
Asked Dec 12, 2019
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The number of people afflicted with the common cold in the winter months dropped steadily by 25 each year since 2002 until 2012. In 2002, 8,040 people were inflicted. Find the linear function that models the number of people afflicted with the common cold C as a function of the year, t. When will less than 6,000 people be afflicted?

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Expert Answer

Step 1

As ‘C’ denotes the number of people afflicted with common cold and let ‘t’ be the years after 2002 where year 2002 is denoted by t=0. The given information can be written as.

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dC = -25 dt dC = -25dt

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Step 2

On integrating we can find a linear function of ‘C’ with respect to ‘t’ as.

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ſdc = [-25dt C =-25t +c,

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Step 3

Using the initial conditions given the spec...

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t = 0, C = 8,040 8,040 = -25(0)+c G = 8,040 C =-25t +8,040

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