Thread: Rate of change

I'm pretty familiar with the calculator settings but I don't know how to answer these questions. It would be appreciated if you would show me the steps in how you answer these questions.

1. The per-share dividends for Wachovia Corporation increased from $1.38 in
1995 to $2.06 in 1999. Assume that the rate of change was constant.

(a) Using data points of the form (x, dividend), where x is the number of
years since 1995, determine whether a linear function describing this
information would be a direct variation. Why or Why not?


(b) If the function describing this information is in the slope-intercept form,
what is m and what is its interpretation?




2. Gateway manufactures and sells computers. This company's scale rose from $5.0 billion in 1996 to 10.4 billion in 2000. Assuming a constant rate of
increase, find the average rate of change in sales during this period.

I entered 0 (representing 1996) & 4 (representing 2000) in my L1 column corresponding to 5.0 and 10.4 under L2 in my calculator . I got 1.35 as the average rate of change in sales. Is that correct?

Originally Posted by Ash

I'm pretty familiar with the calculator settings but I don't know how to answer these questions. It would be appreciated if you would show me the steps in how you answer these questions.

1. The per-share dividends for Wachovia Corporation increased from $1.38 in
1995 to $2.06 in 1999. Assume that the rate of change was constant.

(a) Using data points of the form (x, dividend), where x is the number of
years since 1995, determine whether a linear function describing this
information would be a direct variation. Why or Why not?

we have (x1, dividend1) = (0,1.38) and (x2, dividend2) = (4, 2.06)

the slope between these two points, m = (dividend2 - dividend1)/(x2 - x1)
=> m = (2.06 - 1.38)/(4 - 0) = 0.68/4 = 0.17

using the point-slope form, we can find a linear function for the information:

y - dividend1 = m(x - x1)
=> y - 1.38 = 0.17(x - 0)
=> y = 0.17x + 1.38 ...........this is the linear function

this is not a direct variation, since two quantities vary directly if one quantity is a constant times the other. that is, if x and y are our quantities then for direct variation we must have:

y = kx, where k is a constant. you see here that is not the case, we have y = kx + c, where k and c are constants (k happens to be the slope, which we call m)

(b) If the function describing this information is in the slope-intercept form,
what is m and what is its interpretation?

i suppose m is what you are calling the slope. as you can see, we found it above (these questions were asked in the wrong order!). i'm not sure exactly what you are looking for in this answer but i can tell you, since m is positive, we have increasing dividends with each passing year, the increase is constant

Originally Posted by Ash

2. Gateway manufactures and sells computers. This company's scale rose from $5.0 billion in 1996 to 10.4 billion in 2000. Assuming a constant rate of
increase, find the average rate of change in sales during this period.

I entered 0 (representing 1996) & 4 (representing 2000) in my L1 column corresponding to 5.0 and 10.4 under L2 in my calculator . I got 1.35 as the average rate of change in sales. Is that correct?

you are correct