Question

Which of the following equations represents an account that will double after approximately 6 years? y = 1(1.50)^x y = 2(1.17)^x y = 4(1.06)^x y = 3(1.12)^x

Answer 1

Answer: The correct answer is y = 3(1.12)^x.

One way to find this answer is to use the "Rule of 72". It states that if you divide 72 by the rate it will give you the approximate number of years an investment will take to double.

If you divide 72 by 12 you get 6, meaning it will take about 6 years. In the answer we select, the rate of increase is 1.12 or adding 12%.

Answer 2

The equation y = 3(1.12)^x will double after 6 years. 

In order to find this, we need to test all of the numbers in the parenthesis to the 6th power and see which comes closest to 2. We know that after 0 years, each equation will simply have the value of the number outside of the parenthesis, so we need the number inside to be 2 in order to get it to double. The following are each number in the parenthesis raised to the 6th power. 

1.50^6 = 11.39
1.17^6 = 2.57
1.06^6 = 1.42
1.12^6 = 1.97

Since the one with 1.12^6 is closest to 2, it is the one that nearly doubles after six years.