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### Doubling Time

```
Date: 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

Rule 0f 72
http://mathforum.org/dr.math/problems/vasseur1.26.99.html

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

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
```
Associated Topics:
High School Exponents
High School Interest

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