Question

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.

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

Answer 1

fish the fisherman introduces to the lake.

Answer 2

Months(x) PopulationP(x)
0 -
1 -
2 -
3 -

Answer 3

Describe how to create the exponential function represented by your table. Use complete sentences and arrive at a final exponential function, P(x).
Using your exponential function, P(x), explain the meaning behind each of the numbers and variables in terms of the invasive fish species.
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.
The National Fish and Wildlife Foundation has asked you to calculate when the population of the fish reaches 500. Show all of your work.
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.