Question

I need the answer and the work it asks for

Answer 1

EXPLANATION

Let's see the facts:

Number of bees = 1500

Decreasing rate = 12% = 0.12 (in decimal form)

Number of flowering plants = 800

Number of removed plants/month = 25

Part A:

Function for the number of bees:

y = a (1-r)^x

Where a= initial population = 1500 r=decay rate in decimal form

Replacing terms:

`y(t)=1500(1-0.12)^t`

Function for the number of flower plants throughout the months.

In this case, we know to consider that there is a decreasing of 25 plants by month:

g (t)= 800 -25t

Part B:

After 6 months, we would have,

#Bees:

y(6) = 1,500(0.88)^6

= 1,500*0.46

= 696 bees

#Plants:

g(6) = 800 - 25*6

= 800 - 150

= 650 flowering plants

Part C:

Here we need to equal both equations:

y(t)= 1,500*(0.88)^t= 800 - 25t = g(t)

We can plug differents values of t until both equations are equal.

#5

1,500*(0.88)^5= 800 - 25*5

791.59 > 675

#6

1,500*(0.88)^6= 800 - 25*6

696.6 > 675

#7

1,500*(0.88)^6= 800 - 25*6

613 < 675

The solution is between 6 and 7. Let's try with 6.5 months:

1,500*(0.88)^6.5= 800 - 25*6

653 < 675

Thus, the solution is greater than 6.5 but smaller than 7. Hence, we can affirm that the number of months is equal to 7.