Question 184656
the number of bacteria in a culture increased sixfold in 10 hours.
 Assuming natural growth, how long did it take their number to double?
:
:
Let x = hourly growth constant
:
1(x^10) = 6
10*log(x) = log(6)
10*log(x) = .778
log(x) = {{{.778/10}}}
log(x) = .0778
x = 1.1962
:
Find the time in hrs to double (t)
1.1962^t = 2
t*log(1.1962) = log(2)
.0778t = .301
t = {{{.301/.0778}}}
t = 3.869 hrs to double
;
:
Check solution in calc: enter 1.1962^3.869 = 1.9999~ 2