Question

Biologists notice an alarming trend in the walleye population in Lake Erie. Despite annual restocking rates of 2 million fish, the population is decreasing by 15% each year. They estimate the walleye population was 26 million at the beginning of the current year. Write a sequence to represent the population for the first 4 years. (remember the restocking amount)

Is this sequence geometric or arithmetic? How do you know?



Walleye populations are considered to be in a rehabilitation state when they are between 15 and 20 million. In what year will the population reach this level? In addition to a harvest restriction, what intervention could be used?



What will the population of walleye be in year 8?


Using the formula the sum of the population for the first 10 years?

Answer 1

f(x) = 26000000(.85)^x + 2,000,000

f(1) = 26,000,000

f(2) = 24100000

f(3) = 22485000

f(4) = 21112250

Geometric, it is going down by a %, not a fixed number

Year 5, less pollution

f(8) = 9,084,753.65

Explanation:

f(2) = 26,000,000 (.85)^2 + 2,000,000

f(2) = 24100000

f(3) = 26,000,000 (.85)^3 + 2,000,000

f(3) = 22485000

f(4) = 26,000,000(.85)^4 + 2,000,000

f(4) = 21,112,250

f(8) = 26,000,000(.85)^8 + 2,000,000

f(8) = 9,084,753.65