Question

Diff EQ question: A colony of bacteria initially has 100,000 members. After 6 days, the population has decreased to 80,000....

There is more to the question, but could someone check my work?

I've got: \[P _{0} = C = 100,000\] and, since we know P(6) is 80,000, we can say: \[80,000 = 100,000e ^{-6k}\]

To solve, I divided the right-hand side by 100,000, giving me: \[.8=e ^{-6k}\] finally, taking logs of both sides and dividing to isolate k I got: \[\frac{ \ln(.8) }{ -6 }=k\]

Answer 1

did I do this right?

Answer 2

Seems to be correct.

Answer 3

Feels too easy.. thanks for taking a look.