Question 271545
the population of a colony of bacteria is growing exponentially according to the function below , where t is the time in hours. how long will it take for the population of the colony to grow to 1,000 B(t)=12*e^0.2t
:
{{{12*e^(0.2t)}}} = 1000
{{{e^(0.2t)}}} = {{{1000/12}}}
Use the nat logs
{{{ln(e^(0.2t))}}} = {{{ln(1000/12)}}}
{{{.2t*ln(e)}}} = {{{ln(1000/12)}}}
nat log of e is 1, so we have
.2t = 4.22848
t = {{{4.22848/.2}}}
t = 22.1142 hrs to reach 1000
;
Check on a calc using t=22.1142
enter: 12*e^(.2*22.1142) = 999.99 ~1000