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April 22nd, 2014, 03:44 PM   #1
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Math instructor help

Ello all, I am current mechanical engineering major and i also teach math at a private high school. Currently, i have an interesting question. Bare in mind i know how to solvew the problem, but what i am wanting is how they came up with the equation.

Ok, so according to nasa, the total number of astroids after 1990 can be represented by a(t)=77(1.283)^t

where t is in years

Ok so here is my question. what does the 77 stand for and who figured out that if you take that 77 and multiply it by 1.283^t you will get a estimate for how many asteroids there are. IE

let t be 16 years you get roughly 4000 astroids

or

4000=77(1.283)^t

divide by 77, take ln of both sides and you get 15.9=t. ok cool. easy to solve, but HOW did they come up with that equation?

thanks
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April 22nd, 2014, 04:34 PM   #2
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I assume they took the number of asteroids located by year, took the logarithms, and did a linear fit.
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April 22nd, 2014, 05:47 PM   #3
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AWESOME. ok so here is my next question.

when you say they performed the logs on it, what exactly do you mean. Lets say they see 50 astroids in a year?

See here is my issue, im in calc 3 and diff eq and all through my carer in math, we never were taught how to do that kind of real application. so this is kind of new to me. I can solve solve solve and solve all night long, but to take real data like that and perform logs on it is new.

thanks
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