Question

a culture of bacteria contains 10000 bacteria initially. after an house the bacteria count is 25000. find the doubling time to the nearest minute.

Answer 1

i am going to make a guess that "house" is an hour

Answer 2

yes oops!

Answer 3

ok we can do this a couple ways, but the snap way is this

Answer 4

\[25000\div10000=2.5\] set
\[(2.5)^{\frac{t}{60}}=2\] and solve for \(t\)

Answer 5

i put a 60 in the denominator to convert the units from hours to minutes at the beginning. we could have converted at the end
no matter

solve via
\[\frac{t}{60}=\frac{\ln(2)}{\ln(2.5)}\] and so
\[t=\frac{60\times \ln(2)}{\ln(2.5)}\] and a calculator

Answer 6

45.39

Answer 7

you can also model this as
\[1000e^{rt}\] and then you have to find \(r\) and then the doubling time, but it seems like a large waste of time to me, since the numbers i used in the expression
\[(2.5)^{\frac{t}{60}}\] i got from reading, not computing

Answer 8

seems like a reasonable estimate to me

Answer 9

so then to figure out how many bacteria would be there after 3 hours, you would do what?

Answer 10

the model is \[1000\times (2.5)^{\frac{t}{60}}\]

Answer 11

you mean 10000 right

Answer 12

for 3 hours replace \(t\) by 180 or if you are working in hours compute
\[10000\times (2.5)^3\]

Answer 13

oh yeah i guess it is 10000
i missed a zero

Answer 14

156,250

Answer 15

hope it is clear how i arrived at \((2.5)^{\frac{t}{60}}\) almost instantly
the population increased by a factor of \(2.5\) in 60 minutes

Answer 16

yeah it is thank you

Answer 17

that answer cannot be right

Answer 18

oh maybe it is, let me check

Answer 19

yes, it is right, sorry

Answer 20

ok