Over a certain period of time, a precious metal doubled in price every 6 years.What was the yearly percentage growth rate for the price of this metal during this period? Round your answer to two decimal places if necessary.
A) 33.79%
B) 12.25%
C) 12.75%
D) 33.33%

Question

Over a certain period of time, a precious metal doubled in price every 6 years.What was the yearly percentage growth rate for the price of this metal during this period? Round your answer to two decimal places if necessary. ​
A) 33.79%
B) 12.25%
C) 12.75%
D) 33.33%

Quizplus · Accepted Answer

The yearly percentage growth rate can be calculated using the formula for compound interest: $P = P_0(1 + r)^t$, where $P$ is the final price, $P_0$ is the initial price, $r$ is the rate of growth, and $t$ is the time in years. Given that the price doubles every 6 years, we set $P = 2P_0$, $t = 6$, and solve for $r$. Rearranging the formula gives us $2 = (1 + r)^6$. Taking the sixth root of both sides gives $1 + r = 2^{1/6}$, which simplifies to $r = 2^{1/6} - 1$. Calculating this gives a rate of approximately 0.1225 or 12.25% per year.

Over a Certain Period of Time, a Precious Metal Doubled