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

A= bees: f(t) = 1500 × (0.88)∧t plants: g(t) = 800 - 25×t

B: (Bees) 1500 × (0.88)∧6= 696.60 After 6 months (696 bees ): 800 - 25×6 = 650 (Flowering Plants)

C: 1500 × (0.88)∧t=800 - 25×t

t = 6.779965672

After 6 months: 650 flowering plants

Explanation:

A= bees: f(t) = 1500 × (0.88)∧t

plants: g(t) = 800 - 25×t

B: (Bees) 1500 × (0.88)∧6= 696.60

After 6 months (696 bees ):

800 - 25×6 = 650 (Flowering Plants)

After 6 months:

650 flowering plants

C: 1500 × (0.88)∧t=800 - 25×t

t = 6.779965672

it will take around 7 months for the bees and the plants.

Answer 2

So the answer to this question is:

A= bees: f(t) = 1500 × (0.88)∧t
plants: g(t) = 800 - 25×t

B: (Bees) 1500 × (0.88)∧6= 696.60
After 6 months (696 bees ):
800 - 25×6 = 650 (Flowering Plants)
After 6 months:
650 flowering plants

C: 1500 × (0.88)∧t=800 - 25×t
t = 6.779965672

Answer is it will take 7 months or 6 for the bees and the plants.
Hope this helps!