Doubling TimeDate: 03/08/2002 at 14:50:39 From: Ariele McWhinney Subject: Scientific math formula In my science lesson this week they are talking about the doubling time of the human population and other things. I have a formula that has DT standing for doubling time: DT = 70(or any other #...I used x)/% growth per unit time I am very confused. I kind of understand the formula, but then they give me problems to figure out: If the cost of an all-day ski lift ticket at Colorado's Vail Ski Area has been growing at about 7% per year ever since Vail opened in 1963, and at that time the cost of a ticket was $5, what did it cost in 1993? I have tried replacing the information that they give me in the formula, but I don't know which part of the formula to replace it with. Ariele McWhinney Date: 03/08/2002 at 16:06:05 From: Doctor Rick Subject: Re: Scientific math formula Hi, Ariele. Here is a hint on finding things on Dr. Math. You can use the Search Dr. Math form http://mathforum.org/mathgrepform.html to search for words or a phrase relating to your question. For instance, if you type in doubling time and select "that exact phrase" to look for these words together as a phrase, you'll find this answer: Rule 0f 72 http://mathforum.org/dr.math/problems/vasseur1.26.99.html Here you will read about your formula, why it (sort of) works, and when it doesn't work. The number in the formula does matter, and it should be about 72; but the formula is only an approximation. The exact formula is DT = log(2)/log(1+p/100) where p is the percentage increase per unit time. Thus, in your example, p=7, so 1+p/100 = 1.07 and DT = log(2)/log(1.07) = 10.245 years However, this doesn't directly solve your problem, which says nothing about doubling time. Instead we can write this equation: C = 5(1.07)^t where C is the cost of a lift ticket and t is the number of years since 1963. Do you understand this equation? At t= 0 (the year 1963) the cost is $5: C = 5(1.07)^0 = 5(1) At t = 1 (the year 1964) the cost is 1.07 times $5; that's an increase of 7%. Each year following, you multiply by another factor of 1.07. You can find the cost of a lift ticket in 1993 by deciding what the value of t is in that year, then plugging this value into the equation in place of t, and evaluating it to find C. I'll be glad to answer any questions my explanation has raised. I don't know how much you understand, so I haven't tried to explain everything; I'll expect you to ask if you need more detail on some point. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ Date: 03/08/2002 at 16:31:39 From: Ariele McWhinney Subject: Scientific math formula Thank you very much for your explanation; it will help me greatly. I think that my dad and I can do the rest. I am in algebra this year and just getting into complicated formulas. Thank you again, Ariele McWhinney |
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