Question

The net profit of a company for the years 2000 to 2011 is approximated by the function p(t) = t³ – 5tÆ + 6t, where p is the profit (in thousands of dollars) and t is the number of years that have passed since January 1, 2000. For which period will the company report a net loss?

Answer 1

Can someone please help

Answer 2

is that "Æ" symbol a typo?

Answer 3

refresh if you get a bunch of weird symbols

Answer 4

Its 5t^2 thats what its supposed to be

Answer 5

oh ok, so

\[\Large p(t) = t^3 - 5t^2 + 6t\]

right?

Answer 6

yes

Answer 7

are you in calculus class?

Answer 8

no. Im on a online math class (12th) grade

Answer 9

Im taking math 3

Answer 10

alright, then the best way to do this is to graph p(t)

I recommend you use this graphing calculator

https://www.desmos.com/calculator

Answer 11

type in x^3 - 5x^2 + 6x into the calculator

Answer 12

okay

Answer 13

when is the curve below the x axis? for which x values?

keep in mind that x >= 0

Answer 14

its below the x-axis between the positive 2 and 3

Answer 15

correct

Answer 16

x corresponds to the number of years after the year 2000

Answer 17

since 2 < x < 3 is when p(t) is below the x axis, this means

the company has a net loss between 2002 and 2003

Answer 18

so the answer is ' January 1,2002-December 31,2002 ?

Answer 19

well on Jan 1, 2002, the p(t) value is actually 0

this is because p(2) = 0. There is no net profit and no net loss

the next day is when the losses start happening and they continue to happen until Jan 1, 2003. On this day, you break even again because p(3) = 0. Everything after t = 3 is a net profit

Answer 20

So I'd say from Jan 2, 2002 to Dec 31, 2002 is when you'd have a net loss

Answer 21

Thank you soooo much : ) I have one more question

Answer 22

alright

Answer 23

Which statement about the graph of the rational expression
x^2+6x+9 / x^2-4

Answer 24

seems like an incomplete question

Answer 25

function is above the x axis between -2 and 2.

function is above the x axis and x is greater than 2.

function is below the x axis for x is less than -2.

function is below x axis between -3 and -2

Answer 26

Do I use the graphing calculator?

Answer 27

so graph (x^2+6x+9)/(x^2-4) using desmos and you should see the answer (or at least eliminate the nonanswers)

Answer 28

yes you would

Answer 29

How do I divide using the graphing calculator? I'm using the / symbol but it's making the 9 the numerator instead of dividing the whole equation

Answer 30

you need to put parenthesis around the whole numerator

Answer 31

same with the denominator

Answer 32

(numerator)/(denominator)

Answer 33

which is why you type in (x^2+6x+9)/(x^2-4)

Answer 34

ok I used the ( )

Answer 35

so what answers do you see? or what answers can you eliminate?

Answer 36

We can eliminate anything below the x axis?

Answer 37

lets go through the answer choices

Answer 38

"function is above the x axis between -2 and 2"

is that true or false?

Answer 39

ok

Answer 40

false

Answer 41

why is it false

Answer 42

which parts aren't above the x axis?

Answer 43

I'm looking at it again. One moment

Answer 44

Honestly, I'm not sure exactly what I'm looking at. Is it quadrant 3?

Answer 45

well notice between x = -2 and x = 2 the entire portion of the graph is below the x axis

not above

so that's why A is false

Answer 46

OK, that makes sense. Let me look at b.

Answer 47

I'm assuming B is supposed to say "function is above the x axis when x is greater than 2."

instead of "function is above the x axis and x is greater than 2."

Answer 48

b would be true

Answer 49

yes it is, when x > 2, the curve is above the x axis

Answer 50

choice C
"function is below the x axis for x is less than -2."

true or false?

Answer 51

true

Answer 52

why true?

Answer 53

is the curve below the x axis when you are to the left of x = -2 ?

Answer 54

No it isn't. That's false.

Answer 55

correct

Answer 56

finally choice D
"function is below x axis between -3 and -2"

true or false?

Answer 57

false

Answer 58

so the answer is b

Answer 59

yes because the portion between x = -3 and x = -2 is above

Answer 60

yes it is B

Answer 61

THANKS FOR YOUR HELP!!!! : )

Answer 62

you're welcome

Answer 63

Can you help with another question?

Answer 64

sure