Question

I have a confusing Algebra assignment I really do not understand, it is decently long. Any help would be appreciated!

Answer 1

@phi Please help me out!

Answer 2

@jigglypuff314

Answer 3

@jigglypuff314 @sleepyhead314 QH help :)

Answer 4

If anyone is actually looking at this, for the first part asking for f(x), I got the equation x(1.1)^3-1, I don't know if this is correct or not.

Answer 5

the exponent should be x.
the leading number (where you have x) should be between 2 and 12

Answer 6

Hello and Thank you for asking a Qualified Help question ^_^

Might I ask what point you tried using? :)

Answer 7

You are right Phi, my bad, It should be 3(1.1) ^ x-1 (3 being my number I chose between 2-12) is that correct?

Answer 8

yes. as a check, when x is 1, you get 3 * 1.1^0
but 1.1^0 is 1 (anything to the zero power is 1)
and you get 3*1 or 3
so the first day you get 3

Answer 9

That makes sense, so the answer to Create the exponential function, f(x), that represents the number of packing peanuts found on the beach each day would be 3(1.1)^x-1

Answer 10

yes. though I would put in parens, like this
f(x) = 3(1.1)^(x-1)

Answer 11

Okay thank you, that's what I put. I can do the graphing myself. But there are 5 other parts to this question, now I know thats a lot, but do you think you would be able to help me with the rest of this assignment?

Answer 12

@phi

Answer 13

the next part is graph the line v(x)

Answer 14

Yes correct, it says to use the function v(x) = 1/4x + 14, I thinkk I would plug in 3 as X?

Answer 15

to plot a curve, you find points on the curve i.e. pick an x, and find the y using the equation. but with a line, you only need two points, and draw a straight line through them

Answer 16

I would use x=0 (easy to do)
and x=4 (because 4/4 is a nice integer)

Answer 17

the exponential is more painful. It is not straight, and you will get fractions.

Answer 18

maybe you can use geogebra or other software

Answer 19

so it would then look like:
1/4(0) + 14 = 14
1/4(4) + 14 = 15

is that right? or am I completely butchering that.

Answer 20

yes, so two points on v(x) line are (0,14) and (1,15)

Answer 21

so I've plotted that, would that be correct?

Answer 22

the first number (x value) is the day. you did it backwards

Answer 23

careful! (x, y)
x would be how much left or right
and y is how much up or down :)

Answer 24

and after you plot the two points, draw a line through them

Answer 25

Ah okay, i see what I did there. Let me fix that.

Answer 26

Okay, so when they ask Explain what the solution means in terms of ecological crisis, would it be that the amount of volunteers helping to clean up the packing peanuts does not suffice to the amount of packing peanuts found on the beach?

Answer 27

If you plot the line v(x) and the exponential curve f(x), you will see that v(x) is "above" f(x)
but at around day 20 or 21, f(x) goes above v(x). that means for the first 20 days, the clean up stays ahead of the problem. But after day 20, the pollution comes faster than they can take it away

Answer 28

This is what I put, I am trying to say this stuff in my own words!

When looking at the graph, f(x) is the exponential curve, and one can see that v(x) falls above f(x). From that, one can see that during days 20 and 21, f(x) goes above v(x), meaning that until the first 20 days, volunteers clean the packing peanuts up faster than they litter the ground, after that, the pollution arrives faster than the volunteers can clean up.

Answer 29

yes. but you should show how you know the curves where the curves cross.
in other words, solve for x, from
\[ \frac{1}{4} x +14 = 3 \cdot (1.1)^{x-1} \]

Answer 30

Okay, I will, thank you! Let me take a picture of part two now, this is such a long assignment I'm sorry!

Answer 31

btw, here is the graph for part I

Answer 32

There is no easy way to solve the ugly equation I posted up above, but we can read off the graph the point where the curve and line cross.

Answer 33

Yes, that is exactly what I need, thank you!

Answer 34

So looking at the next question, it asks to create a sine function t(x) that represents the tide, I believe it would be 3 sin (pi/3x) + 4 ????

Answer 35

because 3x would be the 3 feet from normal high or low

Answer 36

ok, but why add 4?

Answer 37

no wait, I mean add 3, because that is the number of packing peanuts I started with. I think, sine questions confuse me.

Answer 38

they just want a sin for the tide (no peanuts)

Answer 39

so
t(x) = 3 sin( stuff)

Answer 40

So would that mean I would choose a number for the normal tide???

Answer 41

I would pick 0 for the "normal height"
that would be someplace on the beach where the water is 0 depth at "mid-tide"

Answer 42

next, what is the "period" of the sin wave (in hours) ?

Answer 43

Okay wait so then the equation would be 3 sin + 0???

Answer 44

or 3 sin (3pi/x) + 0

Answer 45

yes, but we don't have to show adding 0

Answer 46

now we have to fix up your 3 pi/x

first step: what is the period for the tide to go one "cycle"?

Answer 47

24 hours

Answer 48

no, that is two periods hi,lo,hi,lo

Answer 49

or would it be 12, because it is saying high then low, high, low

Answer 50

No wait, it would be 6 hours because it is saying there are 4 tides during the 24 hours, and 24/4 = 6

Answer 51

yes, 12 hours. They don't say if we should measure in hours or days. In part I they had x measuring days. Let's use x in days. so the period is 0.5 days
we use this form:
\[ \sin \left( \frac{2 \pi}{T} x\right) \]
where T= 0.5

Answer 52

one period of a sin wave looks like this