Question

The population of organism A doubles every 3 hours, while population of organism B triples every 5 hours. Suppose the two organisms have equal populations at the start. When will the population of organism A be 10,000 more than that of organism B?

A little help pls :)
I already made an equation of this, sort of, but i just dont know how to simplify or something, it's confusing. Or maybe i did it wrong, so pls anyone? HELP :)

Answer 1

mateaus ur back:)

Answer 2

yey someone's replying! haha :)

Answer 3

3y=2x for every 3 hours (y) = A doubles = 2x. 3(1)=2(1) --> 3=2 , 3(2)=2(2) --> 6=4...

Answer 4

5y=3x for the second one and then find when A will be 10k more than B

Answer 5

@Mateaus there's a formula for this right?

Answer 6

hmm no this involves exponential growth
\[\large 2^{t/3} = 3^{t/5} +10,000\]

Answer 7

@dumbcow i got it like that but the only difference is mine's right side is: 3^t/5 x 10, 000.

haha i think im wrong though

Answer 8

i equated it from the initial population.

Answer 9

wait do we know what the initial population is ? that will affect the answer

Answer 10

also is there a typo...is it "10,000 more" or "10,000 times more" ?

Answer 11

\[from P = Po (2)^{t/3}\]
\[i did \it like this: PO = \frac{ P }{ 2^{t/3} }\]

and did the same for organism B then equated both equations :)

Answer 12

they have the same initial pop :)

Answer 13

@dumbcow they have the same initial population :)

Answer 14

right but what is that initial population?

Answer 15

@dumbcow sorry for the typo!! haha, it's "start"

Answer 16

?? no ...
is it "10,000 more" or "10,000 times more" ?

Answer 17

10,000 more

Answer 18

ohhhhh so im wrong bcoz i multiplied it!

Answer 19

right and it makes it lot harder to solve

Answer 20

what's running in my mind is "10K more" woo haha

Answer 21

uhmmm right :)

Answer 22

i will try again

Answer 23

you cant solve it algabraically, i suggest using newtons method for finding zeros or wolframalpha.com

Answer 24

or a graphic calculator

Answer 25

do you know answer by chance, that may clear up this confusion on setting up the equation

Answer 26

also if you are adding the 10,000 you need to know what the initial population is

Answer 27

@dumbcow im using logarithm or natural log :)

Answer 28

our teacher is allowing us to use scientific calculator

Answer 29

wont work if adding the 10,000....now im thinking it should be multiplied :{
can you check the wording of question in book again

Answer 30

okay :) wait.

Answer 31

@dumbcow double checked it. that's really the question..

Answer 32

and our teacher didn't mention to us what the answer is :(

Answer 33

ok then they wrote it wrong....it should say "10,000 times more"
\[2^{t/3} = 10,000*3^{t/5}\]
this you can solve by using logs...the initial pop cancels

Answer 34

ohh that's what i did at first because what's running in my mind was "10K more" Hahaha

Answer 35

as i said, (below the problem i submitted) i came up with an equation in which i dont know how or it's hard to simplify, and that was THAT equation. :)

Answer 36

my problem is about the two bases of the both with exponents

Answer 37

i dont rly have the idea, i dont know, my brain is empty hahaha

Answer 38

haha ok we've come full circle...anyway
\[\frac{t}{3} \ln 2 = \frac{t}{5} \ln 3 + \ln 10,000\]
did you get this far

Answer 39

i didnt hahaha, i was stuck the one said lol

Answer 40

oh!! natural log.

Answer 41

right and 2 rules of logs are
\[\ln (a*b) = \ln a + \ln b\]
\[\ln (x^{n}) = n \ln x\]

Answer 42

ohh i forgooot lol

Answer 43

i lack knowledge in natural log :( rly.

Answer 44

@dumbcow uhm, can you simplify your equation for me plss :D

Answer 45

you will need to learn those rules before the test...almost every exponential equation is solved using logs

Answer 46

yah i really need to :(

Answer 47

ok move the like terms to 1 side, then factor out variable "t"
\[t(\frac{\ln 2}{3} - \frac{\ln 3}{5}) = \ln 10,000\]
last step is divide
\[t = \frac{\ln 10,000}{\frac{\ln 2}{3} - \frac{\ln 3}{5}}\]

Answer 48

sci cal! haha

Answer 49

= 813.16 (sci cal )

Answer 50

@dumbcow so is it, 813.16 hours? :)

Answer 51

yep

Answer 52

@dumbcow Thank you very much for your time!! :) Hope u have a nice day!! :D

Answer 53

yw , you as well
good luck with your class

Answer 54

thanks :)