Question 55172
The population P of a certain culture is expected to be given by a model {{{highlight(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. Find the value of r if the population is expected to reach 200 in 3 days.
P=200 and 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))}}} Use this rule to rewrite the equation: {{{highlight(ln(a^m)=mln(a))}}}
{{{ln(2)=3rln(e)}}} Remember this rule {{{highlight(ln(e)=1)}}}
{{{ln(2)=3r(1)}}}
{{{ln(2)=3r}}}
{{{(ln(2))/3=3r/3}}}
{{{(ln(2))/3=r}}}
{{{.6931471806/3=r}}} You need a scientific calculator for that.
{{{.2310490602=r}}}
Round off to wherever your asked.
Happy Calculating!!!