after t hours:
count of A = 10000(1.08)^t , where t is in hours
count of B = 33000(.94)^t
when is the count the same ?
10000(1.08)^t = 33000(.94)^t
1.08^t = 3.3 (.94)^t
take log of both sides
log 1.08^t = log 3.3 + log .94^t
t log1.08 = log 3.3 + tlog .94
t log 1.08 - t log.94 = log 3.3
t(log 1.08 - log .94) = log 3.3
t = log 3.3/(log 1.08 - log .94)
= appr 8.6 hours
state your conclusion
At noon, Professor Simon has a petri dish with 10,000 cells of Bacteria A. In another petri dish, he
has 33,000 cells of Bacteria B. Every hour, Bacteria A grows by 8%. Every hour Bacteria B cells die off,
decreasing the number of cells by 6%. After how many hours will there be more cells of Bacteria A than of
Bacteria B?
1 answer
1 answer