Please Assist Constant Percent Change
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Question

Please Assist Constant Percent Change 
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anonymous · Answer

attachment

anonymous · Answer

I just need help with B.

tkhunny · Answer

$0.65^{n} < 0.01$

A logarithm or two will get you there.

anonymous · Answer

I don't understand...

tkhunny · Answer

Then I would have to guess that you do not understand the equation given in Part A.  True?

tkhunny · Answer

It is a typical slight misdirection.  We are told that 35% disappears each year.  We cannot use this information directly.  We must translate it to 65% remains each year.  100% - 35% = 65%

One Year
$0.65^{1}=0.65=65$%

Two Years
$0.65^{2}=0.4225=42.25$%

Four Years
$0.65^{4}=0.17850625=17.85$%

Eight Years
$0.65^{8}=0.0318644812890625=3.18$%

We can play this game and fish around for the 1% solution, or we can just solve for it directly, using logarithms.

Are we getting closer?

tkhunny · Answer

Well, then, $0.65^{n} = 0.01 \implies n = \dfrac{log(0.01)}{log(0.65)} = 10.690$

10 years still will not achieve 1%, but 11 years will.

$0.65^{10} = 0.01346274334462890625 = 1.34$%
$0.65^{11} = 0.0087507831740087890625 = 0.87$%

It is a beautiful thing!

anonymous · Answer

Thank you for walking me through it @tkhunny

tkhunny · Answer

I would sure love to see you do one.  I did all the heavy lifting on this one.