### Home > PC > Chapter 7 > Lesson 7.2.3 > Problem7-67

7-67.

A common tool used to approximate the doubling rate of an exponential function is “The Rule of 70.” Given the annual rates below, solve for the time it takes for the amount to double under exponential growth. Round your answers to the nearest year.
The first one is started for you:
$\left. \begin{array} { l } { a ( 1.02 ) ^ { x } = 2 a } \\ { ( 1.02 ) ^ { x } = 2 } \end{array} \right.$

1. $2\%$

Continue taking the log of both sides.

1. $5\%$

1. $7\%$

1. $10\%$

1. What is “The Rule of 70?”

'The Rule of 70' is called as such because the number of years to double is close to $70$ divided by the annual percent growth rate.