The amount of oxygen released by the tree grows at a rate of 12% per year, but the tree cannot generate more than 6000 pounds of oxygen per year. So, the function should grow by 12% each year until it reaches a maximum value of 6000 pounds per year.
Therefore, the correct sequence to model the description is:
a) f(n) = 1.12f (n - 1) if f(n-1) < 6000
where:
- f(n) is the amount of oxygen released in pounds in year n
- f(n-1) is the amount of oxygen released in pounds in year n-1
The initial value is f(1) = 250 pounds, which is the amount of oxygen released by the tree in its first year.
Option (a) represents this sequence correctly. It says that the amount of oxygen released in year n is 1.12 times the amount released in year n-1, but only if the amount released in year n-1 is less than 6000 pounds.