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

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