Question

Mr. Fredlin harvests oranges from his orange tree every year. The tree produced 75 pounds of oranges in its first crop. As the tree has matured since its first crop, the weight in pounds, , of the orange harvest has increased exponentially by 45% each year according to the function w (t)=75(1.45)^t , where is the number of years since the first crop. Based on this model, how many pounds of oranges is the tree expected to harvest in 4 years (rounded to the nearest whole pound)?

Answer 1

Explanation:

The weight of the orange harvest is given by the function:

w(t) = 75(1.45)^t

where t is the number of years since the first crop.

To find the expected weight of the orange harvest in 4 years, we need to evaluate w(4):

w(4) = 75(1.45)^4

w(4) ≈ 213.98

Rounding this to the nearest whole pound gives:

w(4) ≈ 214 pounds

Therefore, the tree is expected to harvest approximately 214 pounds of oranges in 4 years according to this model.