Question

please help me!! fan and medal!!

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

Answer 1

@sunshine201

Answer 2

@uri @perl @samson245

Answer 3

@sunshine201

Answer 4

@PJtheVet

Answer 5

@campbell_st

Answer 6

this is just like the compound interest formula

the growth formula for Oak trees,

A = future population, P = initial population, r is the growth rate n = number of years

\[A = P(1 + \frac{r}{100})^n\]

the pine trees are in decline... so its a depreciation formula

\[A = P(1 - \frac{r}{100})^n\]

the letters are identical to the growth situation... except the difference is growth contains a + and decline contains a -

so substitute the information into each equation.

so if you are having to graph them let y = A and x = n

hope it helps

Answer 7

So wait i have a question would i change the percents to decimals and put them for 4 and then plug in certain years?

Answer 8

@campbell_st

Answer 9

@campbell_st i tried from years 1 to 10 and they never ever reach around the same amount of trees.

Answer 10

ok... so the simplified version of the 2 models are

oak

\[y = 50\times(1.15)^x\]

pine

\[y = 800 \times (0.95)^x\]

so they are the 2 equations...in the 1st quadrant.

graph the 2 equations... the point in intersection will be the time needed for the 2 tree populations to be equal in size