Hello Darya,
Since this is a continuous compound interest problem, we may use the A = P* e^(rt) formula, where A is the new amount after interest, P is the principle (starting) amount, e is the constant (≈2.71), r is interest rate, and t is time. What we are looking for in this problem is the time it takes to double, so we must solve this equation for t.
In this problem we are given: A, P, and r. So plugging in what you have, knowing A=2P (since it's doubled!) We get 2P = P e^(10% *t), and, again, we want to solve for t.
Dividing through by P and remembering that 10% = 1/10, gets us:
2= e^(t/10).
Could you solve it from here?
