Assuming the current trend continues, estimate the annual re

They give me the equation c(x) = 0.19x^-0.657x + 16.6 They also give me a graph, but I think what matters for this exercise is the equation. The exercise asks me:

a) Assuming the current trend continues, estimate the annual rent per square foot in 2004

b) In what year was the annual rent per square foot a minimum?

c) Estimate the minimum annual rent per square foot.

I already looked the answers in the book, but I only got the right answer for part (c). I don't know what equation to use to answer parts (a) and (b). I tried using the Quadratic Formula, but that didn't give me the correct answer.

Could someone please help me find the equation to use? Thank you!

The equation appears to be "c(x) = 0.19x^-0.657x + 16.6". Is this correct?

What does "x" measure? What does "c" measure? How do they relate to parts (a), (b), and (c)?

You say you obtained the answer for part (c). How?

You say you got the wrong answers for parts (a) and (b), using the Quadratic Formula. What did you do, specifically? What answers did you get?

Please be specific. Thank you.

Eliz.

The equation is c(x) = 0.19x^-0.657x + 16.6, and does not contain exponents.

The exercise doesn't say what c measures, but x is the number of years from 1991. The following is what the excercise says exactly, previous to those 3 questions:

Renting office space: the following graph indicates that the price of renting office space in 50 major U.S. states. Markets has been on rise in the recent years, the function is c(x)= .19x^-.657x+16.6 can be used to estimate the annual rent per square foot where x is the years since 1991

Click to expand...

Possibly I'm using wrongly the symbol, ^; in this case -- 0.19x^-0.657x+16.6 -- I meant 0.19 x to the second power

I obtained the answer c using this formule:

. . .y = [4(a)(c) - b^] / [4(a)]

. . .[4(0.19)(16.6)] / 0.76 = 16

By using the quadratic formule, I got this results:

. . .[0.657^0.0361 - 4(0.19)(16.6)] / 0.76

By the way, I am using the symbol "^" to indicate a square root.

Continuing:

. . .[12.75 + 0.65] / 0.76 = 17

. . .[12.57 - (-65)] / 0.76 = 15

Thank you
___________________
Edited by stapel -- Reason for edit: restoring formatting

You say you're using the carat symbol, "^", to indicate both squaring and taking a square root. It can't stand for both. You say that "^" does not indicate exponents, but this is the standard meaning of that symbol in this context.

Do you mean any of the following by your equation?

. . . . .c(x) = 0.19x² - 0.657x + 16.6

. . . . .c(x) = sqrt[0.19x] - 0.657x + 16.6

. . . . .c(x) = sqrt[0.19]x - 0.657x + 16.6

. . . . .c(x) = 0.19x² - sqrt[0.657]x + 16.6

Or do you mean something else?

Since the exercise says that the function c(x) is used to estimate annual rent (cost) per square foot in year 1991 + x, then c(x) has been defined to stand for the cost.

What is the "formula" you are using for part (c) of the exercise? What are "a" and "b" in this context? Is "c" the function c(x), or something else? How does this relate to the exercise and/or the function c(x)?

How does the Quadratic Formula relate?

What do your computations stand for? How do they relate to the exercise? Are you still working on part (c), or do these computations relate to some other part of the question? (Note: Your values for the simplifications are incorrect.)

Please reply with clarification. Thank you.

Eliz.

This is the equation c(x) = 0.19x2 - 0.657x + 16.6 (the first one you typed)

the formula I used to get answer C was

y = [4(a)(c) - b^] / 4(a)

and I used the quadratic formule because I didn't know what any other formule to use
thanks for your help.

dieggo said:

This is the equation c(x) = 0.19x2 - 0.657x + 16.6 (the first one you typed)

Click to expand...

So, in standard notation, c(x) is 0.19x^2 - 0.657x + 16.6.

dieggo said:

y = [4(a)(c) - b^] / 4(a)

Click to expand...

Okay, but what formula is this? Where are "y", "a", and "b" coming from? Is this "c" the same as "c(x)", or something else? And are you using the carat symbol here as a square, an indicator of some unnamed power, as the square root, or as something else?

a) Given that "x = 0" stands for the year 1991 (according to the exercise), what x-value stands for the year 2004? Plug this x-value into c(x), and find the estimated cost.

b) Find the vertex (not the x-intercepts) of the quadratic (parabola). The x-value gives the number of years after 1991. Add this to "1991" to find the year.

c) Once you have the minimizing x-value, plug this into c(x) to find the minimum cost.

Eliz.