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)

(10 points)

n=6.77 months (exactly)

n=7 months (nearest integer, less accurate)

Step-by-step explanation:

A) The initial number of bees in a colony is 1500. Each month the number of bees decreases by 12% which means each month we must factor by (1-0.12)=0.88

So the number of bees as a function of n months is  

1500*0.88*0.88...0.88 (n times)

The initial number of flowering plants is 800 and there are 25 fewer of them each month. It can be written as

B) After 6 months (n=6) there will be

And there will be

flowering plants

C) We want to know the value of n that make B = P:

Rearranging

This equation cannot be solved by exact procedures, we must approach the answer or use any numerical method to solve for n

The best value to solve the equation is n = 6.77 months in which case

And flowering plants

If we wanted to use only integers for n, then we should use the nearest integer to our previous value, that is, n=7. In this case,

flowering plants

the answer is b.)

< 1=< 2

the multiples of 15 are 15, 30,45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195,   210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375,   390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, and 735.

the factors of 15 are 1, 3, 5, and 15.

hope that , fam!

-une, your fren : )