SOLUTION: Michael purchases a rare coin for $100 that will double in value every 9 years. His friend John purchases a rare book for $75 that will double in value every 6 years. If both purch

Question 128802: Michael purchases a rare coin for $100 that will double in value every 9 years. His friend John purchases a rare book for $75 that will double in value every 6 years. If both purchases were made at the same time, in how many years will they be of equal value??? Please HELP me :)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Michael purchases a rare coin for $100 that will double in value every 9 years. His friend John purchases a rare book for $75 that will double in value every 6 years. If both purchases were made at the same time, in how many years will they be of equal value???
--------------------------
Coin DATA:
Value = 100*(2^t/9)
---------------------
Book DATA:
Value = 75*(2^t/6)
--------------------------
EQUATION:
value = value
100(2^(t/9)) = 75(2^(t/6))
2^(t/6-t/9) = 100/75
2^(3t/54) = 4/3
2^(t/18) = 4/3
Take the log of both sides to get:
(t/18)log(2) = log(4/3)
t/18 = 0.4150
t = 7.47 years
===================
Cheers,
Stan H.
RELATED QUESTIONS
A rare coin is purchased for $400 in 2001. Its value increases by 8% each year. About how (answered by checkley77)

Issac has a collection of coins he knows that he has 100 rare dimes and about half As (answered by macston)

The central exhibit at last years big book fair was a display of seven special rare... (answered by stanbon)

Your friend purchases a $165,000 house. If he makes a 20% down payment, how much money... (answered by addingup)

Hi I'm having some trouble finishing this problem, can you help me? thanks Between... (answered by checkley71)

Dr. Aberli recently found 400 pounds of the rare substance, stutzium, in the tunnels... (answered by jorel1380)

Tom purchased a rare stamp for $9 000. He was guaranteed that the stamp would increase in (answered by richwmiller,Fombitz)

In a rare coin collection, there is one gold coin for every three non-gold coins. 10 more (answered by stanbon)

Clyde purchases a new car for $18000.If the car's value depreciates by 8% annually, what... (answered by stanbon)