You know that y = 24*2^(x/77)
just solve
24*2^(x/77) = 100000
2^(x/77) = 25000/3
x/77 = log2(25000/3)
Now finish it up.
A culture of bacteria triples every 𝟕𝟕 minutes. How long will it take a culture originally consisting of 𝟐4 bacteria to grow to a population of 𝟏𝟎𝟎 𝟎𝟎𝟎 bacteria? Round to one decimal place, if necessary.
4 answers
oops. 100000/24 = 12500/3
Count = a(3)^t, where t is a multiple of 77 minutes
100,000 = 24(3)^t
3^t = 4166.666..
take log of both sides, and follow log rules
t = log 4166.6666../log3 = 7.5867 multiples of 77
= 584.178 minutes
= 9.736 hours or 9 hours and appr 44 minutes
I could have used k/77 hours as my exponent and
found k to be 584.178 minutes, (the actual calculations would remain the same)
100,000 = 24(3)^t
3^t = 4166.666..
take log of both sides, and follow log rules
t = log 4166.6666../log3 = 7.5867 multiples of 77
= 584.178 minutes
= 9.736 hours or 9 hours and appr 44 minutes
I could have used k/77 hours as my exponent and
found k to be 584.178 minutes, (the actual calculations would remain the same)
nice catch, Reiny. I misread the growth factor. But I'm sure you caught that, right, Sara?