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

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