A squirrel population grows according to the equation P(t)=2000-1900e^(-0.17t),t in years.the population approaches a limiting value.how long does it take population to reach 90% of this limiting value?

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Answer 1 · 2018-03-05T14:07:57

The time is #=13.24 " years"#

We need

#lim_(x->+oo)e^(-x)=0#

The population is

#P(t)=2000-1900e^(-0.17t)#

The limiting value is

#L=lim_(t->+oo)P(t)=lim_(t->+oo)(2000-1900e^(-0.17t))=2000-0=2000#

as

#lim_(t->+oo)1900e^(-0.17t)=0#

#90%# of this limiting value is

#=0.9L=0.9*2000=1800#

Therefore,

#2000-1900e^(-0.17t)=1800#

#-1900e^(-0.17t)=-200#

#e^(0.17t)=1900/200=9.5#

#0.17t=ln(9.5)#

#t=(ln9.5)/0.17#

#t=13.24 y#