If tuition at a college is increasing by each year, how many years will it take 6.6% for tuition to double?

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Answer 1 · 2017-01-22T20:24:36

It will take #10.845....# years to double

Let current tuition rate be #t#

Then we need the condition #2t#

Using the same model as for compound interest but setting final value after n years as #2t#

#2t=t(1+6.6/100)^n#

Divide both sides by #t#

Note that #" "1+6.6/100" " =" " 100/100+6.6/100" " =" " 106.6/100#

#2=(106.6/100)^n#

Taking logs of both sides

Note that #log(a^n)# is the same as #nlog(a)#

#log(2)=nlog(1.066)#

#n=(log(2))/(log(1.066)#

#n=10.845....# years