SOLUTION: Greg bought a gold coin for $9,000. If the value of the ring increases at a constant rate of 1.79% per year, how many years will it be for the ring to be worth $17,978.02?

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Greg bought a gold coin for $9,000. If the value of the ring increases at a constant rate of 1.79% per year, how many years will it be for the ring to be worth $17,978.02?      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 197691: Greg bought a gold coin for $9,000. If the value of the ring increases at a constant rate of 1.79% per year, how many years will it be for the ring to be worth $17,978.02?
Answer by jojo14344(1512) About Me  (Show Source):
You can put this solution on YOUR website!


The increasing rate of Gold Coin follows:
P%2BP%2ARate%28n%29=F, wheresystem%28P=9000%2CRate=0.0179%2Fyr%2Cred%28n=years%29%2CF=17978.02%29

Substituting:
9000%2B%289000%29%280.0179%29%28red%28n%29%29=17978.02
161.10%2A%28red%28n%29%29=17978.02-9000
cross%28161.10%29%2Ared%28n%29=%2817978.02-9000%29%2F161.10=8978.02%2F161.10
highlight%28red%28n=55.73yrs%29%29, let us say 56 years


*One good way to check on this is by graphing.

Let us appoint the following:
x=red%28years%29 & y=red%28Price%29
It follows,system%28x%5B1%5D=0%2Cy%5B1%5D=9000%2Cx%5B2%5D=55.73%2Cy%5B2%5D=17978.02%29
Via Point Slope Form,
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29=%2817978.02-9000%29%2F%2855.73-0%29=8978.02%2F55.73
red%28m=161.10%29

Thru point x%5B1%5D & y%5B1%5D, (0,9000)
y=mx%2Bb, Slope-Intercept Form
9000=%28161.10%29%280%29%2Bb
9000=0%2Bb
b=9000, Y-Intercept

It follows ---> red%28y=%28161.10%29x%2B9000%29, Line Eqn
drawing%28500%2C500%2C-10%2C65%2C-500%2C20000%2Cgraph%28500%2C500%2C-10%2C65%2C-500%2C20000%2C161.10x%2B9000%29%2Cgreen%28line%280%2C17978.02%2C55.73%2C17978.02%29%29%2Cgreen%28line%2855.73%2C17978.02%2C55.73%2C0%29%2Cred%28locate%2856%2C700%2C55.73yrs%29%29%2Cred%28locate%284%2C18600%2C17978.02%29%29%2Cgreen%28arrow%2834%2C14150%2C38%2C13030%29%29%2Cgreen%28locate%2833%2C12500%2Cy=161.10%28x%29%2B9000%29%29%2Cred%28locate%2818%2C700%2CYEARS%29%29%2Cgreen%28circle%280%2C9000%2C.35%29%29%2Cgreen%28circle%280%2C9000%2C.55%29%29%2Cgreen%28circle%280%2C9000%2C.75%29%29%2Cgreen%28locate%282%2C9000%2CYintercept%29%29%29%29



Thank you,
Jojo