$N = N_0 \cdot 2^{t/T}$ — read aloud, N equals N-nought, times two to the t over T. Compare it with the half-life law and you will see the same skeleton: count how many characteristic times fit into the elapsed time, then raise the characteristic factor to that count. Halving uses $\tfrac{1}{2}$; doubling uses 2. Learning one of these has already taught you the other.

And here is the mental-math gift of the chapter. The rule of 72: at $R$ percent per period, a quantity doubles in roughly $\dfrac{72}{R}$ periods. 6% doubles in 12 years; 8% in 9; 9% in 8. It is an approximation — the honest constant is $100\ln 2 \approx 69.3$ — but 72 is chosen because it divides cleanly by 2, 3, 4, 6, 8, 9 and 12, which is exactly the arithmetic you can do at a bus stop. Use it as the estimate, then let $A = A_0(1 + r)^t$ confirm it. An estimate that agrees with your exact answer is the cheapest confidence you will ever buy.