rate per hr. question (rate of learning, in words per hour)

[Guest]

Supose that a foreign language student has learned N(t)=20t-t^2 vocab terms after t hours of uninterrupted study.

b) What is the rate in terms per hour at which the student is learning tat time t=2h.

how do you do this, at first I thought you use the same formula as velocity: [f(x+h)-f(x)]/h but it didn't work out for me, the answer is suppose to be 16terms/h.
Or should I just retry if you ARE suppose to use that formula?

 

[stapel]

I thought you use the same formula as velocity...but it didn't work out for me....

What did you get?

Please reply showing all of your steps. Thank you.

Eliz.

 

[Guest]

[f(2+h)-f(2)]/h
limh->0 [20(2+h)-2+h)^2-[40-4]]/h
limh->0 [40+20h-4+4h+h^2-36]/h
limh->0 [24h+h^2]/h
limh-> 0 24+h
24+0
=24

 

[stapel]

[f(2+h)-f(2)]/h
limh->0 [20(2+h)-2+h)^2-[40-4]]/h

You might want to be a little more careful with your grouping symbols, and show all steps, as this will tend to help you with your signs and such.

. . . .f(2 + h) - f(2)

. . . . .= [20(2 + h) - (2 + h)²] - [20(2) - (2)²]

. . . . .= [40 + 20h - (4 + 4h + h²)] - [40 - 4]

. . . . .= [40 + 20h - 4 - 4h - h²] - [36]

. . . . .= 36 + 16h - h² - 36

. . . . .= 16h - h²

See the difference that clear grouping symbols made? :wink:

Eliz.