I missed several days of my math class and now have no idea what is going on. We're working on Real Population Growth. I tried to figure this problem out myself, but apparently I'm not getting one of the values right because when I check my answer, it isn't correct. The problem is as follows:
Starting from an estimated U.S. population of 305 million in 2009, use the given growth rate to estimate U.S. population in 2059 and 2109. Use the approximate doubling time formula.
The growth rate they gave me is 0.5% for this problem. I set it up like:
Tdoubling = 70/0.5 = 140
(305 * 10^6) * 2^50/140
50 for the 50 years from 2009 to 2059 and I don't think 140 is the correct value but I don't know what else to try.
The correct answer is 391 million for 2059, I just can't figure out how to arrive at it.
Best Answer
The correct calculation for $0.5\%$ growth over $50$ years from $305$ is $305\cdot 1.005^{50}\approx 391.38$. Your expression for the doubling formula is $305 \cdot 2^{(50/140)}$ [note the parentheses-the way you wrote it is $(305 \cdot 2^{50})/140$, very different]. This is about $390.67$, which rounds to $391$ as well.