**Problem : **
If *P* = 300*e*^{2t}, at what time will P=600?

600 | = 300e^{2t} | ||

2 | = e^{2t} |

use natural log to solve for

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} |

After 4 hours,

ln(2) | = 4k | ||

k | = .173 | ||

B(t) | = B_{0}e^{.173t} |

**Problem : **
Find a function that meets the following:

= 0.693y |

Any function for which

= ky |

must be of the form

e^{0.693t} = 0.693e^{0.693t} |

or 0.693

**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} |

At

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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