Question

There are 1500 bees in a colony. Each month, the number of bees decreases by 12%. There are 800 flowering plants in a garden. Each month, 25 flowering plants are removed.
Part A: Write functions to represent the number of bees and the number of flowering plants throughout the months. (4 points)

Part B: How many bees are in the colony after 6 months? How many flowering plants are in the garden after the same number of months? (2 points)

Part C: After approximately how many months is the number of bees and the number of flowering plants the same? Justify your answer mathematically. (4 points)

Answer 1

Part A:Bees:  f ( t ) = 1,500 * 0.88^tFlowering plants: g ( t ) = 800 - 25 tPart B :f ( 6 ) = 1,500 * 0.88^6 = 696.6  ≈ 697
g ( 6 ) = 800 - 25 * 6 = 800 - 150 = 650Part C :f  ( 7 ) = 1,500 * 0.88^7 = 613g ( 7 ) = 800 - 7 * 25 = 625f ( 7 ) ≈  g ( 7 )After approximately 7 months.