1. ## Logarithm word problems

1. The doubling period for a colony of bacteria is 5 days. Initially, there are 20 cells in the culture. What is the approximate growth rate per day?

2. Boris the bone guy finds a rather unusual animal femur buried underneath his porch. Boris did a quick carbon-14 test and determined that 86.2% of the original carbon-14 remained. Approximately how long ago did the unusual animal die?

Thanks

2. 2. Boris the bone guy finds a rather unusual animal femur buried underneath his porch. Boris did a quick carbon-14 test and determined that 86.2% of the original carbon-14 remained. Approximately how long ago did the unusual animal die?
Let's say the half-life of Carbon-14 is 5750 years. The decay constant is

$k=\frac{-1}{5750}ln(2)\approx{-.00012055}$

86.2 % remains:

$.862=e^{-.00012055t}$

$\frac{ln(.862)}{-.00012055}=t=1231.88 \;\ yrs$