Question

this makes no sense. please help.


Using your exponential function, P(x), explain the meaning behind each of the numbers and variables in terms of the invasive fish species.

my exponential function is 10 x 2^x

Answer 1

a lot of stuff doesn't make sense.... lol :P

Answer 2

i understand how to describe the terms & variables but i dont get what it means by the "invasive fish species" part. like...what.

Answer 3

is there stuff before this on the invasive fish species?

Answer 4

no.

Answer 5

that's why im confused 'af

Answer 6

hmmm.... ok then

Answer 7

should i just write down what the terms and variables mean? i just did that for the previous question though.

Answer 8

i found this online...

A fisherman decided to stock his favorite lake with a few fish that are not native to the region. The fish he introduces have no natural predators in the lake and they experience a large exponential growth. The introduction of an invasive species can be very detrimental to an ecosystem and there have already been noted effects. The National Fish and Wildlife Foundation has asked for your help.

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)
0
1
2
3

P(x)

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

yup. thats what im working on.

Answer 10

OOOOOOOOOOOHHHHHHHHHH... OK... give me a sec then...

Answer 11

alright...

Answer 12

10 x 2^x
10 is the coefficient on the variable... this means that there are 10x- 10 fish originally... i think.

and I think the 2 is an exponent.... am i correct?

Answer 13

or is the x an exponent?

Answer 14

p(x) = 10 x 2 ^ x

Answer 15

x is the small number on top. the exponent to the 2

Answer 16

ok

Answer 17

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

Answer 18

so the x is the rate that the number of fish changes. this is unknown, seeing as it is a variable

Answer 19

i need help with number 5. how to tell when the fish population reaches 500

Answer 20

so.... to sum it up...
10 - the original number of fish
x - the rate the amount of fish changes

Answer 21

ok... i can help

Answer 22

x is the times sign, not a variable.

Answer 23

it is?

Answer 24

yes

Answer 25

yes, it is.

Answer 26

i need help with five and six.

Answer 27

please

Answer 28

ok

Answer 29

\[10 \times2^x\]you just use this equation to describe some kind of change.

Answer 30

no... you would plug it in for y; p(x) is equal to y

Answer 31

this is for #5 right?

Answer 32

probably the number of fish.

Answer 33

y = 10 * 2 ^ x

yeah

Answer 34

\[10\times 2^ x = 500\]

Answer 35

for me... at least....

Answer 36

okay but i need to figure out WHEN the fish population reaches 500.

Answer 37

so then you plug in 500 for y and solve for x.
500 = 10 * 2 ^ x
divide by 10...
50 = 2^x
then you solve....
i got 5.64...
this means 5.64 months

Answer 38

does that help?

Answer 39

THANK YOU SO MUCH YES
omg can you help me with number 6?

Answer 40

sure :D

Answer 41

Exponential growth functions are y=bx and the form of logs are y=log5 (x). So, in my function, 5 is b and x is x. So the log would be log_5 (x). To convert it to where it will be a log with a base of 10, I am going to substitute with 5 because that is how many fish are in the population at the end of 1 month. Okay so now we have log_5 (5). Now we can properly convert this. Ln(5)/ln(5)= 1. So we take that and plug it into log_10 (x) and get log_10 (1). And that is how we convert our exponential function into logs...

Answer 42

make sense? or should i simplify it?

Answer 43

at the end of month 1 there are 20 fish in the pond not 5.

Answer 44

months population p(x)
0 10
1 20
2 40
3 80

Answer 45

ohh.. oops...yeah ur right.... soooooo....
let me fix that....
Exponential growth functions are y=bx and the form of logs are y=log5 (x). So, in my function, 5 is b and x is x. So the log would be log_5 (x). To convert it to where it will be a log with a base of 10, I am going to substitute with 20 because that is how many fish are in the population at the end of 1 month. Okay so now we have log_5(20). Now we can properly convert this. Ln(20)/ln(20)= 1. So we take that and plug it into log_10 (x) and get log_10 (1). And that is how we convert our exponential function into logs.

Answer 46

alright thank you so much (: that all makes a lot more sense now.

Answer 47

yeah! you are welcome :D