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

choice b is correct

step-by-step explanation:

we have been given the following system of inequalities;

we are required to graph the solution to the system of inequalities. using a graphing tool, the graph of the system is as shown in the attachment. the continuous line represents the graph of while the dotted line represents .