Question

The National Fish and Wildlife Foundation has asked you to calculate when the population of the fish reaches 500. Show all of your work.
This is my equation:P(x)=10*2^x
Please help me...

Answer 1

anybody?!

Answer 2

@Compassionate

Answer 3

@perl

Answer 4

please could someone help me? @DanJS?

Answer 5

That function is population P at time x

P(x) = 10* 2^x

Answer 6

What information is given in the problem?

Answer 7

one sec.

Answer 8

The part that i get choked up on is number 5.

1.Create the data to fill in the population table. Be creative when selecting the P(x) values, but remember that this is an exponential growth model. Notice that you even need to come up with how many fish the fisherman introduces to the lake.

Months
(x) Population
P(x)
0 10
1 20
2 40
3 80

2.Describe how to create the exponential function represented by your table. Use complete sentences and arrive at a final exponential function, P(x).
3.Using your exponential function, P(x), explain the meaning behind each of the numbers and variables in terms of the invasive fish species.
4.The current exponential function P(x) measures the fish population’s growth monthly. Using complete sentences explain how to find the rate of growth every week.
5.The National Fish and Wildlife Foundation has asked you to calculate when the population of the fish reaches 500. Show all of your work.
6.The computer system you need to input the function into only works in logarithms of base 10. Using complete sentences, explain how to convert your exponential function P(x) in a logarithmic one and then into a base 10 logarithm.

Answer 9

So you did #!1-4 already

Answer 10

and got that p(x) = 10*2^x ?

Answer 11

#1
The general exponential model is

y = A*b^x

you found A and B from the table right?

Answer 12

yea.

Answer 13

lol okay!!

Answer 14

yeah, the data points fit in that equation, it is right

Answer 15

So should i write 500=10*2^x?

Answer 16

P(x) = 10 * 2^x

#5) When (what x), is it when P(x)=500 fish

Answer 17

yeah

Answer 18

so how do i solve it?

Answer 19

ok, i will write words, you type out the equations....

Answer 20

divide both sides by 10 first

Answer 21

500=10*2^x
/10 /10
50=2^x

Answer 22

take log base 2 of everything

Answer 23

\[\log _{2}2^x = x\]

Answer 24

i get 0?

Answer 25

i dont think you can use log base 2 in a calculator, we have to use the change of base formula

Answer 26

wow,slow me

Answer 27

x = \[x = \log_{2}50 = \frac{ \ln(50) }{ \ln(2) }\]

Answer 28

remember that thing?

Answer 29

yea. so i would get 5.64?

Answer 30

no

Answer 31

5.64 months

Answer 32

: )

Answer 33

Thats it right?

Answer 34

yeah, the last question is already answered it looks like, but instead of using log base e, (ln), use log base 10

Answer 35

log base 10 is the 'LOG' button on the calculator

Answer 36

\[\frac{ \log_{10}50 }{ \log_{10} 2 }\]

Answer 37

lol, i know that!!!

Answer 38

oh, beg my pard. lol

Answer 39

i didnt wirte that^. computer is acting up.

Answer 40

Need to transform

P(x) = 10 * 2^x

to a log equation

Answer 41

would it be like log2^x=10?

Answer 42

@DanJS

Answer 43

\[\frac{ p(x) }{ 10 } = 2^x\]\[\log_{2}[\frac{ p(x) }{ 10 }] = x\]

Answer 44

Then they want you to change that to base 10 log

Answer 45

so you would change the 2 and 10 around?

Answer 46

\[x = \frac{ \log _{10}(p(x)/10) }{ \log _{10}2 }\]

Answer 47

the change of base formula thing

Answer 48

yea thats what i mean.

Answer 49

that is the final answer i think

Answer 50

If you let p(x) be any number of fish, then you can use the computer, which can only do base 10 logs, to find how many months that will be

Answer 51

okay!!!! I really appreciate your help DanJS!!! :) your the only one that helped me. really grateful for that :)

Answer 52

you have a medal coming your way,lol

Answer 53

That is what i am here for.. you are welcome

Answer 54

I dont understand how people get confused about logarithms. Not just you, most people.
They are just exponents. lol

Answer 55

\[\log_{b} x = y ~~~~or~~~~~b^y = x\]

log base b of x, means ' b to what power equals x'

Answer 56

lol, true i get confuse on what formula to use. and remembering the order of sequence, yea thats me!!!

Answer 57

not just you, 99% of people. Just think to hard . lol.

Answer 58

yea i do that a lot. when i get the answer. i say to myself, man i knew that!!

Answer 59

Right, but the work to get to the answer is what has you remember things, if someone just told you the answer, you arent going to remember jack s--t

Answer 60

SOOOO true!!!!! lmbo!!!!

Answer 61

I see math sorta like a toolbox of skills. You dont have to remember anything in particular, as long as you know the general landscape. So if you start somewhere, you can work towards something else using what you do remember.

Answer 62

yea. i like your sense of thinking man.

Answer 63

: ) feel free to tag me in more if ya get stuck on anything

Answer 64

will do!! thanks again DanJS!!! :)