Question

use the formula P=Ie^kt. a bacterial culture has an initial population of 10000 . If its population declines to 3000 in 8 hours , what will it be at the end of 10 hours ?

Answer 1

I haven't done one of these in a while but I'm pretty sure it goes something like this:
\[P=Ie^{kt}\]\[3000=10000e^{8k}\]First you need to solve for k:\[\frac{3000}{10000}=e^{8k}\]\[0.3=e^{8k}\]\[ln(0.3)=8k\]\[\frac{ln(0.3)}{8}=k\]\[k=-.1505\]Now that you have k, solve the equation again with the time of 10 hours:\[P=10000e^{(10)(-.1505)}=?\]