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Q: Revenue Problem ( Answered ,   3 Comments ) Question
 Subject: Revenue Problem Category: Science > Math Asked by: tralcva-ga List Price: \$35.00 Posted: 18 Aug 2006 21:52 PDT Expires: 17 Sep 2006 21:52 PDT Question ID: 757538
 ```It's a differential equation of sorts, but beyond that....im not sure what else to do. Because of a slump in the economy, a company finds that its annual revenue has dropped from 742,000 in 1998 to 632,000 in 2000. if the revenue is following an exponential pattern of decline, what is the expected revenue for 2002? (t=0 in 1998)``` Subject: Re: Revenue Problem Answered By: elmarto-ga on 19 Aug 2006 08:12 PDT Rated: ```Hello! If revenue follows an exponential pattern of decline, we should be able to characterize it with a function of the form: Revenue(t) = A * e^(c * t) where: t is time c is a decay parameter A is the level of sales at t = 0 So, first of all, why does A represent the revenue at t = 0? If we plug t = 0 into the equation, we get: Revenue(0) = A * e^(c * 0) Revenue(0) = A * e^0 Revenue(0) = A * 1 Revenue(0) = A Therefore, we've found that in the Revenue(t) equation, A = 742,000 (the revenue of the company when t = 0) We know that 2 years later (at t = 2), revenue has become 632,000. So now we can use this information to find c, the missing parameter: Revenue(2) = 742000 * e^(c * 2) 632000 = 742000 * e^(c * 2) 632/742 = e^(c * 2) ln(632/742) = c * 2 c = ln(632/742) / 2 c = -0.0802299... Therefore, we've found that the revenue function is: Revenue(t) = 742000 * e^(-0.0802299 * t) Now, what's the expected revenue for year 2002? In this case, t = 4. Therefore, we simply plug t = 4 into our equation, getting: Revenue(4) = 742000 * e^(-0.0802299 * 4) Revenue(4) = 538307.33 Expected revenue for year 2002 is thus 538,307.33 I hope this helps! If you have any doubt regarding my answer, please don't hesitate to request clarification before rating it. Otherwise, I await your rating and final comments. Best wishes! elmarto```
 tralcva-ga rated this answer:  `Homework???`
 `It's actually part of a study guide for a final exam`
 ```A much simpler way to think of it would be to simply calculate the compound annual growth rate. [ (Current value / Previous value) ^ ( 1 / n-years) -1 ] Therefore, from 1998 to 2000 the annualized rate is -7.7%. Using this figure, the revenue estimate for 2002 is \$538.3K.``` 