Question

The number of meerkats in a wildlife preserve is modeled by

P(t)= 2520/1+4e^-.2t

where t is the number of years after 2015. When does the model predict that
the meerkat population will reach 2100?

Answer 1

`\tt 2100=(2520)/(1+4e^(-0.2t))\\\\2100(1+4e^(-0.2t))\\\\2100+2100.4e^(-0.2t)=2520\\\\8400e^(-0.2t)=420\\\\e^(-0.2t)=0.05\\\\-0.2t=ln~0.05\\\\t=15\\\\2015+15=\boxed{\bold{2030}}`