ok so it asks....
"The size of an exponentially growing bacteria colony doubles in 8 hours. How long will it take for the number of bacteria to triple? Give your answer in exact form and decimal form."

Question

ok so it asks....
"The size of an exponentially growing bacteria colony doubles in 8 hours. How long will it take for the number of bacteria to triple? Give your answer in exact form and decimal form."

campbell_st · Answer

so your model is 

$$P = P_{0}e^{kt} $$

anonymous · Answer

yes i believe it is. but i'm missing so many variables how do i solve it without$$P _{o}$$

and P @campbell_st

campbell_st · Answer

ok... so the initial population is 1 so it doubles to 2 then t = 8

you need to find the growth constant

so 

$$2 = 1 \times e^{8k}$$

solve for k by taking the ln of both sides

$$\ln(2) = 8k$$

when you know the value of k

set P to 3 and solve for t... 

does that make sense?

anonymous · Answer

Oh snap! nice!

anonymous · Answer

but wait when i have $$3=e ^{\ln(2)/8\times(t)}$$

how do i bring it down and solve. that t confuses me

campbell_st · Answer

thats the way I see the question..

so take the log of both sides... 

$$\ln(3) = \frac{\ln(2)}{8} \times  t$$

campbell_st · Answer

thats why they want an exact answer and a decimal answer...

anonymous · Answer

holy cow! brilliant! thanks!