Please help! A sculpture was purchased for $4,000. The value of the sculpture increases at a rate of 4% per year. After 10 years the sculpture will be worth $5,920.97. In how many years wil the sculpture be worth $10,000? Round to the nearest tenth of the year.

Question

amistre64 · Answer

power went out ....

amistre64 · Answer

A      =   P     (1+ r) ^t  corresponds to:
10000 = 4000(1+.04)^t

now we solve for t

ln(A/P)
------ = t
ln(1+r)

anonymous · Answer

? What does A, P r stand for again?

amistre64 · Answer

i lined up the results  so you could match them up :)

amistre64 · Answer

They are just standard variables in the equations

anonymous · Answer

2.54 years?

anonymous · Answer

This one took me a while to remember how to solve.

Use A = Pe^rt , P= 4000, A=10000, e will cancel with Ln :

10000 = 4000e^0.04(t)

Divide both sides by 4000 to get rid of it...

2.5 = e^0.04(t)

Ln(2.5) = Ln*e^0.04(t)

t = Ln(2.5)/0.04

t = 22.9 years

amistre64 · Answer

that was a good try :)

but the Pert is for "continuous" compounding.  Other than that, you did quite well ;)