Question

a certain bacteria will triple in 6 hours. if the final count is 8 times the original cont , how much time has passed?

Answer 1

*count

Answer 2

let the first count be a
and the next count ar
a,ar,ar^2,ar^3....
\[a_n=ar^{n-1}\]
where n is a period after 6 hours

Answer 3

okay .

Answer 4

\[a_n=a(3)^{n-1}\]

Answer 5

why is r =3 ?

Answer 6

because every time we triple (3) the count,we suppose this occurs every 6 hours

Answer 7

okay.

Answer 8

\[8a=a3^{n-1} \implies 8=3^{n-1} \implies n-1=\log_38\]

Answer 9

so log sub 3 8 isnt my answer ., its what i plug into the calculator ?

Answer 10

yes so how much is n

Answer 11

1.8927892607 ?

Answer 12

+1

Answer 13

in an hour ?

Answer 14

n-1=1,892789607
n=2,89...
thiS mean
we have to multily by 6
17,35h

Answer 15

@RadEn

Answer 16

and so , what would be the final step?

Answer 17

17,35 hours=17 hours 21 minutes