Problem :
If
P = 300e
^{2t}
, at what time will P=600?
600 | = 300e ^{2t} | ||
2 | = e ^{2t} |
ln(2) | = 2t | ||
t | = .347 |
Problem :
A strain of bacteria multiply in such a fashion that they double in number every 4
hours.
Find an expression that describes this kind of growth.
B(t) = B _{0} e ^{kt} |
ln(2) | = 4k | ||
k | = .173 | ||
B(t) | = B _{0} e ^{.173t} |
Problem : Find a function that meets the following:
= 0.693y |
= ky |
e ^{0.693t} = 0.693 e ^{0.693t} |
Problem :
The half-life of a substance is the time that it takes for the mass of that substance to decay
to 50% of its original value. If a certain substance has a half-life of 30 minutes, what is
an equation that describes its decay?
C(t) = C _{0} e ^{kt} |
C _{0} | = C _{0} e ^{k(30)} | ||
= e ^{30k} | |||
ln | = 30k | ||
k | - 0.0231 | ||
C(t) | = C _{0} e ^{-0.0231t} |
Problem :
After 40 minutes, only 34% of a radioactive compound is remaining. What is the
expression describing its decay?
C(t) | = C _{0} e ^{kt} | ||
.34C _{0} | = C _{0} e ^{k(40)} | ||
.34 | = e ^{40k} | ||
ln.34 | = 40k | ||
k | - 0.027 | ||
C(t) | = C _{0} e ^{-0.027t} |
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