How many hours will it take a culture of bacteria to increase from 20 to 2000? Use k= 0.614
1 answer:
Answer:
it will take about 7.5 hours to increase from 20 to 2000
Step-by-step explanation:
y(t) = a e^kt
20 = a e^ kt1
2000 = a e^ kt2
divide these equations
2000/20 = a e^ kt2/ a e^ kt1
when dividing the exponents subtract
100 =a/a e^(kt2-kt1)
factor out the k
100 = e ^ k(t2-t1)
take the natural log on each side
ln(100) = ln (e^ k(t2-t1)
ln (100) = k(t2-t1)
divide by k
ln(100)/k = (t2-t1)
we know k=.614
ln(100)/.614 = t2-t1
7.500277 = t2-t1
it will take about 7.5 hours to increase from 20 to 2000
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