Exponential growth/decay

Jacobpm64

(a) Niki invested $10,000 in the stock market. THe investment was a loser, declining in value 10% per year each year for 10 years. How much was the investment worth after 10 years?

This one isn't tough:
P = P₀a^t
P = 10,000(0.90)¹⁰
P = 10,000(0.348678...)
P = $3,486.78

(b) After 10 years, the stock began to gain value at 10% per year. After how long will the investment regain its initial value ($10,000)?

All right, for this one, I don't know if it means when will the investment get back to $10,000 or when will the $3,486.78 INCREASE by $10,000.

I worked it out as when it would get back to $10,000, but I'm not sure what it's asking for:

P = P₀a^t
10,000 = 3,486.7844...(1.10)^t
2.86797... = 1.10^t
log2.86797 = tlog1.10
t = 11.054..
11.054 years

Also, should I round that up to 12 years? or what?

Thanks in advance.

HallsofIvy

"When will it regain its initial value ($10000)" means when will it once again be worth $10000.

"11.054 years
Also, should I round that up to 12 years? or what?"

Why in the world would you round 11.054 up to twelve years? If you want it to the "nearest year" then round down to 11 years.

Jacobpm64

lol, dunno.. i was thinking in terms of if that number were "people" for some odd reason.. but it isn't... So i'll just keep it as is.. Thanks..