Question

. Find the average rate of change for the investor's plan and the 5-year CD between years 2 and 3, and between years 3 and 5. Explain what this shows in complete sentences

Answer 1

@mathmale

Answer 2

Here's one example:

Find the average rate of change for the 5-year CD between years 3 and 5:

\[ave~rate~of~change = \frac{ change~\in~dollar~amount }{ change~\in~time }\]

Answer 3

Year 3 dollar amount: $5345
Year 5 dollar amount: $5307
Change in time: 5-3 = 2
Find the change in the dollar amount from year 3 to year 5. Hint: use subtraction.
Then divide this result by the change in time (2 years).

What do you get?

Answer 4

19

Answer 5

@mathmale

Answer 6

that's of the right magnitude, but is that a gain or a loss?
Also, Michelle, what are the units of measurement?


"the average rate of change in the value of the 5 year CD from year 3 to year 5 is ... "

Answer 7

Is 19 dollars/year is it a gain?

Answer 8

@mathmale

Answer 9

At the end of year 3 you have $5345. At the end of year 5 you have $5588. does that look like a loss or a gain to you?

Answer 10

It's a gain sorry

Answer 11

Apologies, Michelle! I copied the 2nd figure incorrectly. The
5-year CD amount at the end of year 5 is $5588,

so the change in the dollar amount is $5588-$5345. Calculate that, and divide the result by 2 (years).

does this appear to be a loss or a gain?

What are the correct units of measurement?

Answer 12

It's a gain because from 3 to 5 years your money increases. 121.5 dollars /year

Answer 13

That's perfect. With this background material in mind, you should be able to do the rest of this problem by yourself. congrats!

Answer 14

Wait, I have a question

Answer 15

Note: In every case in which you find an AVERAGE rate of change over an interval, that rate (meaning that slope) will be constant.

Finding the ave. r. of c. over the time period Year 3 to Year 5 will result in a different slope than if you were finding the ave. r. of c. over the time period Year 2 to Year 5.

Answer 16

So it's fine to have different rate of changes?

Answer 17

@math

Answer 18

@mathmale

Answer 19

Michelle, it doesn't matter if one of those functions is exponential. The work done in calculating the 'average rate of change' is precisely the same, and each such 'ave. rate of change' will have exactly ONE value, representing the slope of the secant line connecting one point on your exponential curve to another point on that curve.

Emphatically yes, you WILL obtain different "ave. rates of change" for different time periods. Needless to say, you WILL also obtain diff. "ave. rates of c." for different functions.

Answer 20

So. Just choose one year from another and that'll be my answer?

Answer 21

@mathmale

Answer 22

Not quite. If I ask y ou to find the "ave. r. of c." of so and so function from Year 1 to Year 5, you'd have your work cut out for you:

ave. r. of c.=\[\frac{ Amt~for~Year~5- Amt~for~Year~1 }{ 5-1 }\]

Answer 23

I will tell you the period; you calculate the ave. r. of c.

Or you could create your own sample periods and find the corresponding "ave. rates of c." for each one.

Answer 24

I rather you tell me the periods

Answer 25

I have to get off the 'Net, now. But you could try finding the "ave. r. of c." of Investor B's returns over the period Year 2-Year 5.

Perhaps I'll see you later tonight. thanks for your persistence!!

Answer 26

Ok thanks