The population of rabbits in an area is modeled by the growth equation P(t)=8e^0.26t, where P is in thousands and t is in years. How long will it take for the population to reach 25,000?

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Answer 1 · 2018-06-23T19:21:41

I tried this:

Let us set #P=25# we get:

#25=8e^(0.26t)#

rearrange:

#e^(0.26t)=25/8#

take the natural log of both sides:

#ln[e^(0.26t)]=ln[25/8]#

simplify:

#0.26t=ln[25/8]#

#t=1/0.26ln[25/8]=4.38~~4.4# years corresponding to 4 years and 5 months (more or less)