Question

An oak tree that is 220 years old produced acorns at two different rates. Until it reached maturity, it produced an average of 900 acorns a year. However, once the tree reached maturity, it produced an average of 2200 acorns a year. One particular tree, Angel Oak, has produced about 289,000 acorns in its lifetime. At what age did it reach maturity?

Answer 1

would i add the year and month ?

Answer 2

@Lily2913 @UsukiDoll

Answer 3

@mathmath333

Answer 4

@Redcan

Answer 5

@mayankdevnani

Answer 6

@zzr0ck3r

Answer 7

i just dont get this

Answer 8

\(t_1+t_2=220\) where \(t_1\) is the time that the first tree was young, and \(t_2\) is the time it was mature.

make sense?

Answer 9

wich is 220 years ? for t1?

Answer 10

so a tree grows for 220 years, part of that time it is young, we call that time \(t_1\) and the rest of the time it is old, we call that time \(t_2\).

So \(t_1+t_2=220\)

Answer 11

so divide it by 2 ???

Answer 12

no

Answer 13

I am just asking if you understand that

Answer 14

im sorry i really dont get this

Answer 15

that if we add the time it was young and time it was old we get the total time?

Answer 16

does that make sense/.

Answer 17

okay i get that

Answer 18

so \(900t_1\) is the amount of trees it produces when it is young.

Answer 19

like if it was two years old it gave 1800 trees.

Answer 20

right?

Answer 21

okay right

Answer 22

and similarly we have \(2200t_2\) gives the amount of trees when it is old

Answer 23

if we add these together we have the total amount of trees.

\(900t_1+2200t_2=289000\)

Answer 24

the amount of trees it produced when it was young plus the amount of trees it produced when it was old is 289000

Answer 25

okay i got that, i just dont know find the year

Answer 26

so we have two equations

\(900t_1+2200t_2=289000\\t_1+t_2=220\)

Solve for \(t_2\) in the second equation and you get \(t_2=200-t_1\) right?

We are almost there.

Answer 27

how did you get that ?

Answer 28

\(t_1+t_2=220\) so we just subtract \(t_1\) from both sides and get \(t_2=220-t_1\)

Answer 29

t1 which is 900 ?

Answer 30

no

Answer 31

can you maybe sketch it out

Answer 32

you agreed that \(t_1+t_2=220\) and you also agreed \(900t_1 + 2200t_2=290000\) now all I did was take \(t_1+t_2=200\) and subtract \(t_1\) from both sides.

So now I have

\(900t_1+2200t_2=289000\\t_2=220-t_1\)

Take the second equation and plug it in to the first one.

\(900t_1+2200(200-t_1)=289000\)

Now lolve for \(t_1\)

Answer 33

solve*

Answer 34

the very first line in that should say 289000 not 290000

Answer 35

omg i really dont understand

Answer 36

whats t1 ?

Answer 37

so we have to figure out what t1 and t2 equals ?

Answer 38

So in zzrocks3r's notation, t1 = 0-tm, and t2=220-tm.

Answer 39

tm ?

Answer 40

okay so whats t1 ?

Answer 41

The time the tree is producing 900 acorns/year ---> t1

Answer 42

is there a easier way to do this because im very very very confused

Answer 43

so whats the equation ? and how do i solve it

Answer 44

??

Answer 45

ok ?