Answer:
it will take about 7.5 hours to increase from 20 to 2000
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