Question 134074
We use the formula A = Pe^(rt)where 

A = final balance 

P = original investment 

r = the annual interest rate (as a decimal) 

t = investment time (in years) 

e = a special "calculator number" that serves as the base of the 
nalural logarithm.

Your question:

If $10000 is invested at 6% compounded continously, in approximately how many years will the amount have grown to $15000?

Let A = 15000

15000 = 10000e^(0.06t)

Divide both sides by 10000.

1.5 = e^(0.06t)

Rewrite as a log.

0.06t = In(1.5)

Solve for t.

t = In(1.5)/0.06

t = 6.757751802

Round 6.757751802 to the nearest ones place and we get

t is about 7 years.