Question

In a biological lab, the cell growth rate of two different organisms is tracked and recorded each week. Given the growth rate, the number of organisms can be determined using the following equations:

s(x) = 100 + 23x
m(x) = 90(1.2^x)

Answer 1

@DanJS

Answer 2

You can fill in the table right?

Answer 3

uhhh do i just replace the like 0 with the x and all?

Answer 4

Yeah just put x= 0,1,2,3,4,5 into both and record the values

Answer 5

can u wait while i try it??

Answer 6

is 1.2^0 1?

Answer 7

Here is the graph for both the linear s(x), and the exponential m(x), functions.

Answer 8

:D

Answer 9

I can't do the exponent on the table can u do that for me ?

Answer 10

s(x) = 100 + 23x
-----------------
Points (x , s(x))

(0 , 100)
(1, 123)
(2, 146)
(3, 169)
(4, 192)
(5, 215)

Answer 11

this is b?

Answer 12

Thats confusing like where r we

Answer 13

m(x) = 90*(1.2)^x
------------------------

points (x, m(x))

(0, 90)
(1, 108)
(2, 129.6)
(3, 155.5)
(4, 186.6)
(5, 223.9)

Answer 14

Those are all the values for the table.

Answer 15

wait so what?????

Answer 16

so the table is what? because i need to have 1 and 2 to the table

Answer 17

ahh i think ik

Answer 18

For x=0 to x=5, those are all the values for both of the functions...

Answer 19

i got it :P I understood halfway through my desperate typing xD

Answer 20

Part b, Using the table, where do both functions have the same value...
It is between x=4, and x=5. So approx... when x=4.5 both functions will have the same value.

Answer 21

Because, m(x) goes from being smaller than s(x) , to larger than s(x) between x=4 and x=5, so somewhere in that interval, both functions must intersect and have the same value.

Answer 22

Part c, the graph is linked, but i think they want you to do it yourself on paper, you have to plot each of those points from the table, then draw a line and curve manually.

Answer 23

Here is the graph, you have to label each of the points from the table on the line and curve.

Answer 24

ohhhh so how do i do a curve? and lane EVERY point on what?

Answer 25

and *plot

Answer 26

Draw a graph like the one i linked, label every point from the table on the graph.

Answer 27

like for s(x) , the points are...
(0 , 100) (1, 123) (2, 146) (3, 169) (4, 192) (5, 215)

Answer 28

for m(x), the points are...
(0, 90) (1, 108) (2, 129.6) (3, 155.5) (4, 186.6) (5, 223.9)

Answer 29

ohhhh whats m(x) is that the curve?

Answer 30

The next part d)
From the problem, the X axis values represent the Week #, week 0 (initial value) through week 5

The Y value represents the number of organisms present.

Answer 31

oh ok :P and b i think its just the intersection

Answer 32

Yes m(x) is an exponential equation

Answer 33

oh ok

Answer 34

Each point on the graph (x,y) = (week #, population of organisms)

Answer 35

this is still d ryt?

Answer 36

Part e, to determine the solution from the graph, you estimate the intersection point (x,y)

Answer 37

The last part, you actually have to do the algebra and solve for the exact value for the intersection point...
\[100+23x=90(1.2)^x\]

Answer 38

OMG how on earth do i do that :O

Answer 39

@DanJS

Answer 40

wait so is the exact value the values in the table?

Answer 41

The table are exact values for each function.
the exact value for m(x) = s(x) is not on the table.
(4.433, 201.97) is the decimal approx value for the answer.

Answer 42

ohhhh so how do u figure exact because i can guarantee u don't know xD

Answer 43

divide both sides by 90
take natural log of both sides
...

Answer 44

whats a log?

Answer 45

like natural log xD not a log

Answer 46

log base e

Answer 47

or you can use log base 10, it doesnt matter

Answer 48

:O i have never heard of that how do u do that log base thingy

Answer 49

maybe i should actually look at the lesson xD isn't that like trigonometry ?

Answer 50

@DanJS :( so whats it all mean