Question

ATT James: An agricultural worker in Uganda is planting clover to increase the number of bees making their home in the region. There are a 100 bees in the region naturally, and for every acre put under clover 20 more bees are found in the region

Answer 1

Draw a graph of the total # of bees as a function of x, the number of acres devoted to the clover

Answer 2

What type of function is this?

Answer 3

y=20x+100
where y is bees and x is acres of clover.

Answer 4

I thought it was a line but

Answer 5

total bees intially=100
bee incresease per acre=20
acres=x
total bees=y
y=100+20x
I was almost done anyway, so I posted

Answer 6

K the question continues

Answer 7

Explain both geometrically and algaebraically the shape of the graoh of

Answer 8

The marginal rate of increase in the number of bees with acres of clover

Answer 9

which is N'(x)

Answer 10

You pretty much the geometric part did aleady, but you may as well talk about the intercepts for the algebraic interpretation.

Answer 11

well the marginal rate wld be a straight line like y= whtvr

Answer 12

if
N(x)=20x+100
N'(x)=20
that is the marginal rate

Answer 13

oh ok

Answer 14

so it is a straight line, but a horizontal one obviously.

Answer 15

and then you gotta find the shape of the graph geometrically and algebraically of the number of bees per acre which is N(x)/x

Answer 16

well write it out, what is N(x)/x ?

Answer 17

(100+20x)/x

Answer 18

simplify...

Answer 19

20(5+x)/x

Answer 20

I meant divide to get rid of an x

N(x)/x=20+100/x

Answer 21

so what is the identifying part of this equation in terms of the shape of the graph?

Answer 22

100/x

Answer 23

good, and I assume you know what this looks like, yes?
You can also get the y-intercepts from your eqaution as well. What do you get for that?

Answer 24

sorry, x-intercepts

Answer 25

-5

Answer 26

exactly :) I don't know much to say about the shape besides that. here's a pic
http://www.wolframalpha.com/input/?i=20%2B100%2Fx

Answer 27

ok

Answer 28

I have a question

Answer 29

shoot

Answer 30

what iss the difference btwn the derivative and the average number of bees per acre

Answer 31

one is the average rate of change and the other is the instantaneous rate of change?

Answer 32

No, they reflect different things.

Bees per acre, which is found by simply dividing by x, gives the density of bees in the resulting fields of clover planted.

The derivative tell how many MORE bees you get for each acre planted.

The derivative reflects a rate of change, the number of bees per acre is a density function.

Answer 33

thanks that clarified everything

Answer 34

anytime :)