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



lizzpalmer said:
I'm still working on the calculator

Most of the time I just get error messages

This usually means a "syntax" mistake. For examples, you may have typed a mathematical expression improperly, like a missing parenthesis, or you accidentally typed two plus signs next to each other.

If you post what you did and what the machine displayed afterwards, I will try to help you.


My instructor said I can post on the blackboard anything I need help with and he will answer

I posted 3 days ago questions

the only response I got was another class mate who also can't figure it out

This is typical, with on-line courses.

You'll get better service posting your questions here, instead. 8-)
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you guys have been great! I'm off to court .... I will be home by 5 and will be working on this stuff all night. Thanks for the help!
 
so for the year 1990 energy consumption would be 30.63 quadrillion btus;
for the year 2000 it would be 36.36 quadrillion btus; and
for the year 2008 it would be 41.16 btus

correct?
 
for part b

the average rate of change between 2000 and 2008 would be .584582

correct?
 
for part c:

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

= -4.32x^2 + .028302x + 23.35

not sure on this answer tried to follow the book :)
 


lizzpalmer said:
so for the year 1990 energy consumption would be 30.63 quadrillion btus;

for the year 2000 it would be 36.36 quadrillion btus;

for the year 2008 it would be 41.16 quadrillion btus

These are all correct. :D
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lizzpalmer said:
the average rate of change between 2000 and 2008 would be .584582

To six decimal places, I get 0.599375
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Maybe your result has round-off error.

Did you round-off the values of f(a) and f(b) before putting them into the slope formula?

You should let the calculator carry all of its digits through the steps, and only round the final result.

I would also include the units of rate, when reporting the answer: quadrillion btu/year. 8-)

 


lizzpalmer said:
f ' (x) = -.000144x^3 + .014151x^2 + .1388x + 23.35 Symbol in red is wrong.

The symbol f`(x) represents the first derivative of function f.

What you typed above is the original function f, so you should have written f(x), instead.


= -4.32x^2 + .028302x + 23.35

This is the derivative of f(x), so you should write f`(x) on the lefthand side.

The numbers in red are incorrect.

You correctly reduced the powers of x on those first two terms, but check your arithmetic for (3)(-000144).

Also, the derivative of a constant (23.35) is zero. So, instead of 23.35, you need to take the derivative of the 0.1388x term.
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The function f(x) outputs consumption (in quadrillion btus) for any year.

The function f`(x) outputs the rate at which consumption is changing (in quadrillion btus/year) at any year.

Part (c) wants the rate for 2003. This means that after you determine the correct function for f`(x), you need to input the appropriate value of x for 2003.

Cheers ~ Mark

 
When I do -.000144 * 3 the calculator says: -4.32E-4 so I think I am getting an error.
 


Ah, that's the TI-83's way of showing Scientific Notation.

\(\displaystyle -4.32 \times 10^{-4}\)

The "E-4" part means that you need to shift the decimal point shown in -4.32 four places to the LEFT.

 


lizzpalmer said:
f '(x) = -.000432x^2 + .028302x + .1388 correct?

This is correct. :)
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f`(x) is the rate at which consumption is changing at x years after 1990 (if I remember correctly).

For example, we see by inspection that f`(0) = 0.1388.

This tells us that the rate of change in consumption in 1990 was 1,388,000,000,000,000 btus per year.

f(0) is the consumption itself. 30,634,400,000,000,000 btus were consumed during 1990.

 
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