# Calculus Help Please!!!

A radioactive substance has a half-life of 4 days. Suppose we have 800 mg of this substance.
a) Find the equation of the mass remaining after t days. Use the exact value for k not a decimal
approximation.
b) Rounding your answer to the nearest tenth of a mg, find the mass remaining after 30 days.
c) Rounding your answer to the nearest tenth of a day, find when the mass will be 1 mg.
d) Suppose you do not have any of this substance on hand but that you will need 1000 mg in precisely 36 hours, how many grams should you order right now to insure that you have 1000
mg in 36 hours? Round your answer up
to the “nearest” mg.

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1. The anwser is B

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2. Q = Qi e^-k t
when Q/Qi = 1/2
.5 = e^-k t
ln .5 = - 4 k

so k = (ln .5) / -4
Q = 800 e^ (ln .5)t / 4

k = .1733
so
Q = 800 e^-.1733 t
if t = 30
Q = 800 e^-5.2
Q = 4.4 mg

1/800 = e^-.1733 t
ln(1/800) = -.1733 t

38.6 days

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