Question

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Answer 1

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.
Pine Tree Function Oak Tree Function


Paste Graph Below:










During what year in the future will the park have approximately the same number of pine and maple trees?


How many of each type of tree will there be at that time?

Answer 2

do you want to take a stab at the equations?

Answer 3

yes hold on

Answer 4

Pine Trees
\[f(x) = 800(-0.05x)\]
Oak Trees
\[f(x) = 50(0.15x)\]
I think

Answer 5

almost...

so you know the slopes...and the 800 and 50 are actually the intercepts.

\[p(x)=-0.05x + 800\]
\[o(x)=0.15x+50\]

Answer 6

oh sorry lol

Answer 7

np :)

you confident in your ability to graph those?

Answer 8

yes can you open geogebra files?

Answer 9

i doubt it...no problem, i have faith you'll get it. my recommendation would be to have your x-scale be about 1000...since after 1000 years, the pines will still number about 750 and the oaks will only be 200...still a long way to go before they cross

Answer 10

we need to figure out in what year they two graphs cross...so we do the same thing we did for the beaches...set them equal to each other.

\[-0.05x + 800 = 0.15x + 50\]

Answer 11

ok

Answer 12

solve for x and you get....?

Answer 13

Just in case putting the Graph

Answer 14

x = 3750

Answer 15

nah...i'm on a crappy work computer so i can't open the file.

but your x is exactly right. :)

so after 3750 years, the tree numbers will be the same.

how many onf each tree will there be? (plug 3750 into either equation for x)

Answer 16

612.5

Answer 17

perfect...i'd recommend rounding up to 613 since you can't have half a tree...

Answer 18

yes thank you lol

Answer 19

np :)

Answer 20

@mtbender74 just to clarify its year 3750 right?

Answer 21

well, they didn't give us a staring year, so the best we can say is that it's 3,750 years from now...

Answer 22

we assume they just did the study and counted the initial number of trees...so if it were this year, it would be the year 5764 AD...but i wouldn't put that...just leave it as "in 3,750 years..."

Answer 23

Yes Thank You So Much I Amazingly Appreciate it @mtbender74

Answer 24

Have the Best Memorial Day Weekend Ever!

Answer 25

i get to work, but i'll try :)

Answer 26

have a burger from the grill for me. :)

Answer 27

lol XD