f(x)= -.000144x^3 + .014151x^2 + .1388x + 23.35

L

lizzpalmer

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Ok - I moved on in the world to Differential Calculus.

The question I have is:

Total energy consumption (in quadrillion BTU's) for the US can be approximated by:

f(x) = -.000144x^3 + .014151x^2 + .1388x + 23.35

Where x = 0 corresponds to the year 1970.

a. Find energy consumption for 1990, 2000 and 2008
b. Find the average rate of change in energy consumption between 2000 and 2008
c. At what rate was energy consumption changing in 2008?

Now, I am assuming they want me to use some sort of formula. The problem is there are 40 of them in this chapter or more and I have no idea even how to get started with it.

Any help would be appreciated.
 


lizzpalmer said:
f(x) = -0.000144x^3 + 0.014151x^2 + 0.1388x + 23.35

Where x = 0 corresponds to the year 1970

a. Find energy consumption for 1990, 2000 and 2008

Now, I am assuming they want me to use some sort of formula. Not for part (a)
Click to expand...

For example, the energy consumption for 1990 is the number f(20).

Just do the arithmetic.

For part (b), the average rate-of-change can be interpreted graphically as the slope of the line connecting two those two data points.

Part (c) requires you to determine the derivative of function f. Use the Power Rule for that.

Interesting model. It shows consumption dropping drastically about 35-40 years from now. I wonder why they think that will happen? :wink:

 
Re: f(x)= -1.000144x^3 + .014151x^2 + .1388x + 23.35



lizzpalmer said:
Sorry somehow I posted the problem wrong. it isn

t -1.000144

it is -.000144

Huh?

I see -.000144 in your original post.

I do not see t.

Does "isn" mean "is" ?
Click to expand...

If you click the [Preview] button before clicking the [Submit] button, you can see what your post will look like. This allows you to proofread your typing and correct mistakes before posting.

Cheers 8-)

 
mine shows -1 so that is funny. it is f(x) = -.000144x^4 + .014151x^2 + .1388x + 23.35

Thanks for the hint. I will work out part a and post then move on to part b lol
 
so, for part a I came up with:

1990 = 20.2664 therefore energy consumption would be 20.27 quadrillion btu's

2000 = 1.3699 therefore energy consumption would be 1.37 quadrillion btu's

2008 = 52,708.76836 therefore energy consumption would be 52,708.77 btu's

Does that sound right?
 


lizzpalmer said:
f(x) = -0.000144x^4 + 0.014151x^2 + 0.1388x + 23.35

Is the exponent 4 another typographical error?
Click to expand...

I now strongly suggest that you review your posts before clicking [Submit].

 
Re: f(x)= -1.000144x^3 + .014151x^2 + .1388x + 23.35

for part b:

Average rate of change

The formula I see for this is:

[f(b) - f(a)] / [b - a]

then the slope is (a,f(a)) amd (b,f(b))

but what I'm not sure of is what to put in for a and b?
 
lizzpalmer said:
1990 = 20.2664 Huh?
Click to expand...

In mathematics, sloppy communication is a major roadblock.

I'm sure that you mean f(x) is 20.2664 for the year 1990. Please use complete sentences or proper notation. Otherwise, we spend too much time trying to decipher the intent.

In 1990, x = 20.

f(20) = 30.6344

Your values for the years 2000 and 2008 are also incorrect.

Please check your arithmetic. If you cannot resolve your mistakes, then post your work.

Cheers 8-)
 
I'm sorry, I'm exhausted ... I will re-do in the morning and see what I can come up with. Thank you and have a great night :)
 


lizzpalmer said:
for part b: Average rate of change

The formula I see for this is:

[f(b) - f(a)] / [b - a] ? This is the slope formula

f(b) - f(a) is the difference between two y-coordinates and b - a is the difference between the corresponding x-coordinates


then the slope is (a,f(a)) amd (b,f(b)) ? These are not "the slope"; these are two points

Specifically, those are symbolic representations for the coordinates of two points on the graph of f.
Click to expand...


A pair of numbers separated by a comma and written inside a set of parentheses is called an "ordered pair". We use ordered pairs to write the coordinates of points on the xy-plane.

In other words, (a, f(a)) is just another way of writing (x, y).

You already know that y = f(x), yes? We call that symbol for y "function notation".



In this exercise, symbol a is the x-coordinate of some point on the graph of function f, and symbol f(a) is the corresponding y-coordinate for that point.

Likewise, b is the x-coordinate of a different point, and f(b) is its corresponding y-coordinate.

I'll demonstrate with the data point for 1990. We know that x = 20 and y = 30.6344 for 1990. In other words, the point located at (20, 30.6344) is on the graph of f(x). Therefore, if the ordered pair (a, f(a)) were to represent this point, then symbol a means 20 and symbol f(a) means 30.6344.

For part (b), you want to use the two points that correspond to 2000 and 2008. Find the slope of the line connecting those two points.

The formula says that slope is "the difference of the y-coordinates divided by the difference of the x-coordinates".

f(b) - f(a) is a symbolic expression for "the difference of the y-coordinates".

b - a is a symbolic expression for "the difference of the x-coordinates".

This is why the slope formula can be written as:

[f(b) - f(a)] / [b - a]


Good luck, and goodnight :)

 
I am really trying at this but ... think I speak a different language sometimes lol.

I can't get your answer for the year 1990.

Here's my math, please tell me what I am doing wrong.

year 1990 would be 20 therefore x = 20

f(x) = -.000144x^3 + .014151x^2 + .1388x + 23.35

= -.00144(20)^3 + .014151(20)^2 + .1388(20) + 23.35

= -.00144(8000) + .014151(400) + 2.776 + 23.35

= -11.52 + 5.6604 + 2.776 + 23.35

= 20.2664

Therefore 1990 would have been 20.27 Quadrillion BTU's
 
for year 2000 I would be using x = 30 and for 2008 I would be using x = 38, correct?
 
ok I think I understand the content for part B, as soon as I get the answers right for part a.

Thank you!
 


lizzpalmer said:
f(x) = -.000144x^3 + .014151x^2 + .1388x + 23.35

= -.00144(20)^3 + .014151(20)^2 + .1388(20) + 23.35

= -.00144(8000) + .014151(400) + 2.776 + 23.35

= -11.52 + 5.6604 + 2.776 + 23.35

= 20.2664
Click to expand...

Incorrect values are shown in red

 
if the formula says -.000144 do I not leave it that way ... or am I supposed to ignore the negative?

I'm still working on the calculator lol. Most of the time I just get error messages so it must also speak another language.

My instructor said I can post on the blackboard anything I need help with and he will answer because he checks it every day .... well I posted 3 days ago questions about this problem ... the only response I got was another class mate who also can't figure it out!
 


lizzpalmer said:
if the formula says -.000144 do I not leave it that way

Leave it alone.

The coefficients in a polynomial remain constant.

Hence, the number -0.000144 is a constant. You may not change it.

:!: Your work shows that you changed it from -0.000144 to -0.00144.


am I supposed to ignore the negative

No.

Again, the number -0.000144 is a constant. You may not change it.

If you were to ignore the negative sign, then you would be changing the constant from a negative number to a positive number.

Never ponder whether you may change any constant in a word problem. Those values are fixed throughout the entire exercise.
Click to expand...

 
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