Calculus Student
Franklin & Marshall College
Lancaster, PA 17604-3003
Dear Calculus Student
It's hard to know how to begin this letter, after
all you did. I have to thank you for rescuing me from
that vile murder charge. Although I knew I was
innocent, I was more than a little nervous that others
might not agree - so I owe you a debt of gratitude.
I guess you don't really know much about me, other
than the fact that I'm divorced from a pretty slimy
cop ("Germy Jeremy", my friends call him). I'm a biochemical engineer, and I've been
working on developing
a heterotrophic bacteria which converts waste matter
into energy. This is a fun field of work: converting
trash into energy is a popular idea nowadays, since we
seem to have too much of the former and limited
supplies of the latter. Usually the conversion is
done by burning, but I've been working on a cleaner,
less toxic method. Since you cleared me in that last
situation, I've been hired at a great company - it
rather amazes me that they hired me, seeing as I was
arrested on my way to the job interview. Nonetheless,
they're an open-minded bunch of folk, and I really
want to give them my all.
These bacteria that I've been working on die in
exposure to sunlight, especially ultra-violet, which
means that they're unlikely to be an environmental
contaminant. But if you put them in the dark with a
big, well-mixed tub of wet household trash, they
reproduce (albeit fairly slowly), doubling their
numbers every two months. (Some bacteria, such as E.
coli, double their numbers every 20 or 30 minutes).
And - this is the great part - every time they
reproduce, they give off energy in the form of heat,
which we can harness and convert into electricity.
They generate energy in direct proportion to their
growth rate; so the faster they reproduce, the more
electricity we can make.
Right now I'm in the midst of working on a proposal
for operating an experimental energy site on the banks
of Plum Lake. Our biggest competitor is the King Coal
Company, which certainly isn't known for its
environmental concern. Even if I weren't applying for
the position myself, I wouldn't want a coal company
operating next to our lake. However, my personal
interests make me doubly anxious to get this contract.
The folks at The General Spore are very supportive and
are encouraging me to give this proposal a lot of my
time and (pardon the expression) energy.
The one thing I'm anxious about is making sure that
I'll actually have sufficient bacteria to have the
plant running at capacity within a year of start-up.
I have exactly 125 pounds of bacteria now, in the
freezer; by the end of twelve months, I'll need to
have the bacteria multiplying at a rate of 2.7
tons/month or 180 lbs/day. The trouble is, I don't
know how to figure out how fast they'll be multiplying
by the one-year point. I know that in two months I'll
have 250 pounds, and by six months I'll have one ton
of bacteria, but I have no idea how to get a general
formula for the number of bacteria on, say, the odd
months-much less on days within the month.
Now, I know that this kind of stuff is probably
really trivial to you, seeing as you're in Calculus,
but it confounds me. Seeing as you've gone so far as
to save my neck once already, do you think you could
help me out with this? I just need a general formula
for the amount of bacteria (by weight) on any given
month; and I need a prediction as to whether they'll
be reproducing fast enough on the last day of the
year.
Thanks so much for your past and future help; I
hope I'll hear from you one way or another by October
14.
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