Let

P = $3,000 the principal (the investment)

t = the time in years

r = 0.06 or 6% the annual interest rate

A = $12,000 the future value (the investment will double in size)

The future value formula for continuous compounding is:

A=Pe^(rt)

Plug the values into the formula:

12000= 3000e^(0.06t)

e^(0.055t) = 12000/3000

e^(0.055t) = 4

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t = 23.1 years

It will take 23.1 years for the investment to grow to $12,000.