Question

A cell of some bacteria divides into two cells every 40 minutes.The initial population is 6 bacteria.
(a) Find the size of the population after t hours A cell of some bacteria divides into two cells every 40 minutes.The initial population is 6 bacteria.
(a) Find the size of the population after t hours @Mathematics

Answer 1

6(2/3)^(60t) is wat i got

Answer 2

actually i think its going to be (2/3)t

Answer 3

a) For each cell present at the beginning of the time period, it will yields 2 after 20min, 4 after 40min, 8 after 60min. So the relative growth rate is k = 8

b) P(t) = c0 * k^t = 60 * 8^t
If you need pessimistic evaluation you should take 60 - 1% ~ 59
For an optimistic evaluation you should take 60 + 1% ~ 61

c) After 5 hours, P(t)=60*8^5=1,966,080

d) After 5 hours, the growth rate is P(6)-P(5) = 13,762,560

e) You reach 20,000 cells when 60*8^t=20000, i.e. t*ln(8) = ln(20000/60)
Hence t=2.7936h, i.e. 2 hours 47 min 37s

I don't know if you need to include tolerance in the results of questions c,d,e.
If yes, you get the ranges by redoing the same by changing the value of the initial population.
Hope this help

Answer 4

What do y'all think?

Answer 5

i believe it should be:\[6\cdot(2)^{\frac{3t}{2}}\]

Answer 6

i just want to use y =Ce^(kt)

Answer 7

Look at what I posted! Good Luck!

Answer 8

because you want to to make sense with the data. at t = 0, you get 6, which is the initial data. at t=40 min = 2/3 hrs, you want 12 bacteria, which is what you get if you pug 2/3 into that equation. At t = 80 mins = 4/3 hrs, you want 24 bacteria, which is what you get when you plug t into that equation, etc.

Answer 9

it was 6(2)^(3t/2)

Answer 10

whyy isnt it 2t/3?

Answer 11

in the exponent you want:\[\frac{t}{\frac{3}{2}}= \frac{3t}{2}\]

Answer 12

oh

Answer 13

so When will the population reach 18

Answer 14

oops, i typed that wrong:\[\frac{t}{\frac{2}{3}}=\frac{3t}{2}\]

Answer 15

set it equal to 18? and do the ln thing ?

Answer 16

yep

Answer 17

hey im stuck

Answer 18

3t/28log2=(18-log6)/(2log2)

Answer 19

\[18=6\cdot(2^{\frac{3t}{2}})\iff 3=2^{\frac{3t}{2}}\iff \ln(3)=\frac{3t}{2}\cdot \ln(2)\]\[\iff \frac{\ln(3)}{\ln(2)}=\frac{3}{2}t\iff \frac{2\ln(3)}{3\ln(2)}=t\]

Answer 20

oh alright