How many hours will it take a culture of bacteria to increase from 20 to 2000? Use k = 0.614

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