Question

I award medals!! I need some help with this :) I am not looking for direct answers as that would be cheating. I just need some help :)

Answer 1

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.

Answer 2

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 | Popluation
x | p(x)
______________|_____________________
|
0 |
1 |
2 |
3 |

Answer 3

Would you mind explaining this to me?

Answer 4

@yuubee
@woohoo
@lukas/sujjmers

Can any of you help me?

Answer 5

What math class are you in?

Answer 6

Ahh, okay I get it. It's asking you to make up a graph that shows there's way too many fishes. So i would say maybe come up with a ratio?
Every one month = 5 new fish maybe?

Answer 7

I am in Algebra 2 :)

Answer 8

Sorry @K-K-K-Kiaa! THe server quit on me for some reason. So it is exponential growth so would it be like this?:
0------5
1------25
2------125
3------625

where p(x) is 5*5=25*5=125*5=625

Answer 9

Yes! You got it.

Answer 10

Awesome! Thank you!! I have to create an exponential function to go with it. So would it be like p(x)=5^x?

Answer 11

Yep, that sounds about right (:

Answer 12

Okay! Thank you!! Wow, I am better at this than I first thought lol :) The next step is:
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.

So would the answer be:
The function p(x)=5^x means that the population of fish multiplies by 5 each month. So if you want to the know the population at 10 months, you keep multiplying by 5 until you get to the 10th month and whatever you have then, is how many fish in the populaton at that time.

Answer 13

You are good at this (:
& Yes, perfect wording and everything!

Answer 14

Thank you so much!!! 2 more questions :) The next one is:
The National Fish and Wildlife Foundation has asked you to calculate when the population of the fish reaches 500. Show all of your work.
at 2 months the population is 125 and at 3 months it is 625. So how do I figure out exactly when the population is 500?

Answer 15

Okay @K-K-K-Kiaa, I think I have figured out that one. My answer is The National Fish and Wildlife Foundation has asked you to calculate when the population of the fish reaches 500. Show all of your work.
At the end of 2 months, the population is 125 and at the end of 3 months the population is at 625. We have to find when the population is 500. So what I did was: 500=5^x.Then I set it up like this: x=ln(500)/ln(5). x=3.861353116147.
So the population reaches 500 at about 3.8 months.

Can you help me with the last one please?
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.

I am going to try at it and then post my answer like I have been doing so you can see if it is right. Thanks for all of your help so far!

Answer 16

This is my answer for number 6:
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.