Question

4. A wooded area in a state park has a mixture of different types of trees. There are 800 pine trees and 50 oak trees. The number of pine trees is decreasing at a rate of 5% per year. The number of oak trees is increasing at a rate of 15% per year. If these trends continue:

Write two functions to model this situation and graph those two functions on the same coordinate grid.

Answer 1

Don't worry about graphing, just help me with the equations. :)

Answer 2

multiply 85/100 by the number of oak tress to get the number the next year. multiply 95/100 by the number of pine trees to get the number the next year.

Answer 3

Thanks @DavidUsa , do you think you could help me with the equations? :) How would you write an equation for 800 pine trees decreasing at a rate of 5% per year and another one for 50 oak trees increasing at rate of 15%? :)

Answer 4

The number of pine trees is decreasing at a rate of 5% per year.

the rate is 5% = 0.05
if you start at 1 and decrease by 5% you do: 1 - 0.05 = 0.95

if you start at 800, it would be 800 - 0.05*800= 800 * (1- 0.05) = 800*0.95
the following year, you will start with 800*0.95 trees, and go down by 5% which means multiply by 0.95 = 800*0.95*0.95 or
\[ 800 \cdot 0.95^2 \]
or in general , after n years
\[ 800 \cdot 0.95^n \]

Answer 5

Okay, thanks soo much for that. :) @phi. :)

Answer 6

increasing at a rate of 15%

means the rate is 0.15 and if you start at 1 you would do 1 +0.15*1 = 1+0.15= 1.15
in other words, multiply by 1.15 for each year that goes by

Answer 7

So 50*1.15x?

Answer 8

Thanks soo much, @phi, I appreciate it. :)