1. For all positive integers m, fn(m) = 3m, when m is odd, and fn(m) = (1/2)*m, when m is even. Which of the following is equivalent to
fn(9)*fn(6)? Answer: 27


9 is odd then fn(9) = 3*9 = 27
6 is even then fn(6) = 1/2 * 6 = 3

fn(9)*fn(6) = 27 * 3 = 81


2. When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year? Answer: 2/3

Important : the height of the tree increased by a constant amount each year for the next 6 years. If X is the amout incresead each year.

Then,for the next 6 years we can write : 4+x+x+x+x+x+x = 4 + 6x

At the end of the 4th year : 4 + 4x


At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year => 4+6x = (4+4x) + 1/5*(4+4x)

=> Resolve the equation and obtain x = 2/3