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# Differential Equations/Percent lost formula

Question
Hi,

I need to formula to calculate something like this

if I have 5000 dollars and loose 5% of it per DAY. How many days is it going to take to have 10 dollars left in my pockets.

I used powers as in 10 = 5000*.95^n and tried to find x, an got somewhere between 121 and 122.
5000    0.95    122    \$ 9.58
5000    0.95    121    \$10.08

First, divide by 5000 and get 0.002 = .95^n.
Then, take ln() of both sides and get ln(0.002) = n*ln(.95).
Finally, divide by ln(0.95) and get n = ln(0.002)/ln(0.95).
This gives n = 121.1582951.  That is the same as 121 days, 3 hours, and 48 minutes.
That is actually 47.94495422 minutes, but 48 is close enough.

Now interest is probably done once a day, so after 121 days, there is \$10.08,
One more day puts it at \$9.58.

Differential Equations

Volunteer

#### Scott A Wilson

##### Expertise

I am capable of solving most ordinary differential equations and a few not so ordinary, but those are few and far between.

##### Experience

I have taken Differential Equations at OSU. Occasionally I have assisted people with questions on the subject.

Publications
I wrote a thesis on the study of shock waves and rarefaction fans. That occurs in nature when mathematics fails to apply. See, mathematics says that when shock waves appear, there should be two solutions whereas nature knows there is only one way to be in that area. When rarefaction fans occur, the mathematics says there should be no solution, but despite this, nature still moves ahead with its own plan.

Education/Credentials
I received an MS degree at OSU in Mathemematics and a BS degree at OSU in Mathematical Science.

Awards and Honors
I graduated from OSU with a Bachelor of Science degree in mathematics with honors. Two years later, I graduated from OSU with a Master of Science degree in mathematics with honors. Between these two degrees, I have more hours in graduate courses that required to get them.

Past/Present Clients
I answered many questions at OSU, down in south seattle at a college, at a church in Corvallis, OR, as Safeway in Washington, and many other areas. I have answered over 8,500 right here, but only a little over 190 of them have been in differential equations.