Question

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:

Answer 1

@jim_thompson5910

Answer 2

write what you have so far

Answer 3

f(x)=800-5?

Answer 4

*50

Answer 5

thats all i have :( because I'm always confused with functions they don't make much sense to me

Answer 6

how many pine trees do we start with?

Answer 7

800

Answer 8

we have the number of pine trees decreasing by 5% each year

so we subtract 5% of 800 from 800

800 - (5% of 800) = 800 - 0.05*800 = 800*(1-0.05) = 800*0.95

basically we take 95% of 800 to get the next value

Answer 9

i have these functions right y = 800(.95)^x
y = 50(1.15)^x

Answer 10

good, you nailed both

Answer 11

now for B?

Answer 12

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

Answer 13

The answer is 16 and 14.5 years right? but idk how to get to that answer

Answer 14

one sec

Answer 15

probably the best way is to graph both y = 800(.95)^x and y = 50(1.15)^x and look for when they cross

Answer 16

do you have a graphing calculator?

Answer 17

no i never had one :(

Answer 18

this is b right?

Answer 19

ok you can use something like desmos

https://www.desmos.com/calculator

Answer 20

it's a free online graphing calculator

Answer 21

omg xD i have tried that countless times and it always shows that little red line in some random place

Answer 22

but let me try

Answer 23

what did you type in?

Answer 24

y=800(.95)^x

Answer 25

zoom out until you see a red line

Answer 26

it should be a curve actually

Answer 27

k i see it now so the second one

Answer 28

do i put it a different color and how do i do that

Answer 29

i got that too sorry asking needless questions ok :D I'm done with the graph

Answer 30

it should automatically put it in a different color for you

Answer 31

nope not needless, they're good questions

Answer 32

you can move the graph around by clicking on it

Answer 33

try to see where they cross

Answer 34

you can click the point of intersection and desmos will display (or try to) the point of intersection

Answer 35

(14.51,380.03)

Answer 36

I'm getting the same

Answer 37

the x represents how much time has gone by

the y represents the amount of trees

Answer 38

both values are approximate

Answer 39

so this is B?

Answer 40

it's used to answer B and C

Answer 41

so b is not 16 and 14.5

Answer 42

how are you getting "16 and 14.5"

Answer 43

Im not i just figured i did both Decrease and Increase formulas but I'm wrong

Answer 44

so heres all of what i wrote :D 4.

A.
y = 800(.95)^x
y = 50(1.15)^x

B.
14.5 years

C. 380 tress approximately in 14.5 years

Answer 45

oh i have to graph those 2 functions

Answer 46

for C, they just want the number of trees

Answer 47

but yeah you have the right idea

Answer 48

:D ok so don't write 14.5

Answer 49

yeah I think 380 works fine

Answer 50

ok well Honestly thank you so so so so much :) if i have anymore problems i'll send you a message

Answer 51

you're welcome