Question 1040022
the number of bacteria in a certain culture is given by the function b(t)=10000e^.04t
where t represents time in hours. how long will it take for the number of bacteria to reach 15000. round to nearest hundredth
:
{{{10000*e^(.04t) = 15000}}} 
divide both sides by 10000
{{{e^(.04t) = 15000/10000}}}
{{{e^(.04t) = 1.5}}}
using natural logs
{{{ln(e^(.04t)) = ln(1.5)}}}
log equiv of exponents
.04t*ln(e) = ln(1.5)
the nat log of e is 1. find the nat log of 1.5
.04t = .405465
t = {{{.405465/.04}}}
t = 10.34 hrs to reach 15,000