Question 65737
"The population P of a certain culture is expected tp be given by a model P=100e^rt where r is a constant to be determined and t is a number of days since the original population of 100 was established.  I need to find the value of r if the population is expected to reach 200 in 3 days."
P=200
t=3
{{{200=100e^(r*3)}}}
{{{200/100=100e^(3r)/100}}}
{{{2=e^(3r)}}}  Take the natural log of both sides
{{{ln(2)=ln(e^(3r))}}}  remember: ln(a^m)=mln(a)
{{{ln(2)=3rln(e)}}}
{{{ln(2)=3r(1)}}} remember: ln(e)=1
{{{ln(2)=3r}}}
{{{ln(2)/3=3r/3}}}
{{{r=ln(2)/3}}}
{{{r=.6931471806/3}}}
{{{r=.2310490602}}}  Round off to whatever you are asked for.
Happy Calculating!!!