Last Question!!! I really need help! The number of bacteria in an experiment is increasing according to the law of exponential growth. When there are 250 bacteria, the growth rate is 50 bacteria per hour. Find the proportionality constant.

Question

anonymous · Answer

what's the initial number of bacteria?

anonymous · Answer

are you given that info at all?

anonymous · Answer

It does not say

anonymous · Answer

huh...

anonymous · Answer

I know.  They don't give all the information.  I can show you the answers... if you want

anonymous · Answer

do you know the derivative? My guess is that you have to use it

anonymous · Answer

My lessons did not have any questions like this so I am not sure how to solve it.

anonymous · Answer

I know how to find the derivative

anonymous · Answer

law of exponential growth is y(t) = ce^kt, so the derivative of that is y'(t) = kce^kt

anonymous · Answer

I just don't know what to take the derivative of

anonymous · Answer

oh I know

anonymous · Answer

wait no... it wouldn't work cuz you have 3 unknown variables...

anonymous · Answer

oh, derp :) There's a simple equation that you can use

anonymous · Answer

k, so if you set b=number of bacteria, then db/dt = kb. Just solve for k :)

anonymous · Answer

db/dt = kb, so 50 = k250, so k should be 1/5

anonymous · Answer

Thanks!