Question

Advanced function

Answer 1

ikr

Answer 2

first step would be to substitute x = 40 into the new equation (-0.16x^2 + 21.6x - 400)

Answer 3

new = 208 so the old function has to equal 104

Answer 4

if P(x) = the new function then

old = new/2 so old = (-0.16x^2 + 21.6x - 400)/2

Answer 5

ok

Answer 6

ok bc i cant figure it out at all... while u think im gonna take a quick shower and walk my neighbor home.

Answer 7

ok?

Answer 8

sure

Answer 9

ok thx

Answer 10

I guess we can set

old = 104 = (-0.16x^2 + 21.6x - 400)/2 and simplify to get

208 = -0.16x^2 + 21.6x - 400

which simplifies to

-0.16x^2 + 21.6x - 608

Answer 11

comparing that with P(x) = -0.16x^2 + 21.6x - 400

old = P(x) - 208

Answer 12

so for part a) I end up with two transformation functions,

old = P(x)/2
and
old = P(x) - 208?

Answer 13

and for part b) I would just plug in -0.16x^2 + 21.6x - 400 and simplify?

Answer 14

part d seems like a horizontal transformation by substituting x - 2 for x?

Answer 15

anyway to recap:

Answer 16

part a: function transformations in terms of P(x)

old = P(x)/2
and
old = P(x) - 208

Answer 17

part b: substituting P(x) = -0.16x^2 + 21.6x - 400 to get

-0.08x^2 + 10.8x - 200
and
-0.16x^2 + 21.6x - 608

Answer 18

I think Froppy has the right idea for part a. If you want to verify that those functions work, you can plug (40) in for x, and you'll see that they equal 104 in both cases.

Answer 19

For part b, your first step to simplifying the quadratic equation would be to divide out the common coefficient for each element.
We can take the first equation, -0.16x^2 + 21.6x - 608

Answer 20

If we divide each element by (-0.16) we are left with the equation
-0.16(x^2 -135x +3800)

Answer 21

We can further simplify the binomial inside the parenthesis by observing that 95+40=135, and that 95*40=3800. The function can therefore be simplified as (x-95)(x-35).
If you multiply these elements together using distribution, you will get the binomial above

Answer 22

Altogether, the simplified equation is -0.16(x-95)(x-40)

Answer 23

We can apply the same process to the second equation, P(x)= -0.08x^2 + 10.8x -200

Answer 24

should I do the factoring?

we can factor out (-0.08) to get
-0.08(x^2 -135x + 2500)

Answer 25

idk how to lol

Answer 26

So it looks like that's as far as we can simplify that equation.
-0.08(x^2-135+2500) might be as far as we can go.

Answer 27

The way the question is phrased is a little confusing. "at the time the original version was released" doesn't really suggest any value of (x), other than, as Vocaloid suggested earlier, 0.
We could take this to mean, before any units of the device have been produced or sold.

Answer 28

If we follow this reasoning, it's easy to see that -0.16x^2 + 21.6x - 608 will return a value of (-608) when x=0.
Likewise -0.08x^2 +10.8x -200 will return a value of (-200) when x=0.
Practically, you can think of this meaning that the fixed cost to start marketing the devices is either 608(thousand) dollars in one scenario and only 200(thousand) dollars in the other. In these terms, I think that the latter option is preferable, at least from the beginning.

Answer 29

so for part d am I right in my reasoning that, if 2,000 devices are given away, then we substitute (x-2) for x in the equation? :S

Answer 30

Yes, I agree with you there as well, Froppy.
Since the functions are originally based on the costs and revenues for each thousand units produced and sold, giving up 2000 units would shift the equation to the right by 2 units.
For the "new" function we are given at the outset, we would get
P(x) = -0.16(x-2)^2 + 21.6(x-2) -400... which we can simplify to -0.16x^2 + 22.24x -443.84 by multiplying out all the factors.
Feel free to substitute x for (x-2) with the other two equations to get the new profit functions for those.

Answer 31

it says to write it in terms of P(x) though

Answer 32

so if new profit function after donations = -0.16x^2 + 22.24x -443.84
and P(x) before donations = -0.16x^2 + 21.6x - 400, then:

Answer 33

new = 0.8x + P(x) - 43.84 (?)

Answer 34

So I took "in terms of function transformations and P(x)" to mean, "in the case of the original function and the transformed functions," not that the equation itself has to be written in terms of P(x). But that interpretation definitely makes sense too!

Answer 35

idk yours makes more sense mathematically

Answer 36

I would go with -0.16x^2 + 22.24x -443.84 for d

Answer 37

Oh, and I think we're meant to repeat the process for the "possible original" functions we found as well. That is, replacing (x) with (x-2) for the [-0.16x^2 + 21.6x - 608] version and the [0.08x^2 + 10.8x -200] version. It's a little extra work, but I believe you can do it.

Answer 38

@smithm29 it's a lot of algebra but it's just a substitution

Answer 39

-0.16x^2 + 21.6x - 608

we replace "x" with "x-2" whenever x shows up in the equation

so we get:

-0.16(x-2)^2 + 21.6(x-2) - 608 which you can further simplify using distribution

Answer 40

@Vocaloid my head hurts just looking at it lol

Answer 41

(x-2)^2 = (x-2)(x-2) = x^2 - 4x + 4

Answer 42

so we get:

-0.16(x^2 - 4x + 4) + 21.6(x-2) - 608

Answer 43

do you know how to write an equation for the blue line?

Answer 44

um would it be y=2x?

Answer 45

almost

Answer 46

if our "rise" is 100 for every 5 "run" then our slope should be 20 not 2

Answer 47

so if captivity born = remaining in wild then

20t = 20,000(0.95^t) then we can solve for t

I would just use software for this tbh

Answer 48

so I end up with t = 56.144444 so I would just round to 56

Answer 49

(protip you can also type equations into WolframAlpha to solve them)

Answer 50

anyway, that's part a

Answer 51

we actually did part b, it should be C(t) = 20t

Answer 52

for part c we just add them together

P(t) = 20t + 20,000(0.95^t)

Answer 53

for part d we already found out that captivity breeding = wild when t = about 56 yrs

so I would say that for t > 56 years the breeding program stops the decline in population

Answer 54

for part e, since t = years since 1980 then 2020 - 1980 = 40 so we substitute t = 40 into the equation

Answer 55

if t = 40 then 20t + 20,000(0.95^t) = ?

Answer 56

(use a calc for this one)

Answer 57

as t?

Answer 58

wat

Answer 59

in the eq.

Answer 60

20t + 20,000(0.95^t)

20(40) + 20,000(0.95^40) = ?

Answer 61

what is
The sum of 2ab2 and (-5ab2) is the same as the sum of (-6ab2) and ___?

Answer 62

we're not done with the other problem yet :S

Answer 63

the 2s at the end r _^2

Answer 64

ik but i skipped one earlier and its warning me

Answer 65

i dont wanna forget

Answer 66

2ab2 and (-5ab2) = (-6ab2) + x

add 6ab^2 to both sides

Answer 67

2ab^2 - 5ab^2 + 6ab^2 = ?

Answer 68

3ab^2

Answer 69

good, that's your ans

Answer 70

and the one before that would be 2673

Answer 71

that's not what I got, check your calc

Answer 72

20(40) + 20,000(0.95^40) = ?

Answer 73

make sure you are hitting the exponent button not the multiplication button

Answer 74

got the same thing

Answer 75

https://www.google.com/search?q=20%2840%29+%2B+20%2C000%280.95%5E40%29&oq=20%2840%29+%2B+20%2C000%280.95%5E40%29&gs_l=psy-ab.3...161975.163981.0.164231.3.2.1.0.0.0.55.97.2.2.0....0...1.1.64.psy-ab..0.0.0.wvr1f4B-G5M

Answer 76

ans should be about 3370

Answer 77

anyway for part e we just use our breeding equation C(t) = 20(t) = 20(40) = 800