How Long Will It Take To Double My Money?" With A Deposit Of 3,000 For 9 Years At 6% Interest Rate And Continuous Compounding, What Is The Answer? Round Your Answer To The Hundredth's Place.

For continuous compounding, e^rt gives the multiplier for your money, given an interest rate r and a time interval t.

You want to find t for r=6% and e^rt=2.

2 = e^.06t
Ln[2] = .06t
Ln[2]/.06 = t
.693147/.06 = t = 11.55

It will take 11.55 years at 6% per year to double your money.
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"9 years" has nothing to do with the problem of doubling your money. Nor does $3000. The multiplier for 9 years is

e^(.06)(9) = e^.54 ≈ 1.716007

$3000 will be worth $3000*1.716007 = $5148.02 after 9 years.