Integration Qs: traffic-flow function F(t) = 82 + 4sin(t/2)

[paulxzt]

Any help is appreciated. Thank you.


The traffic flow at a particular intersection is modeled by the function F defined by F(t) = 82 + 4sin(t/2) for 0<equal t <equal 30, where F(t) is measured in cars per minute and t is measured in minutes.

1. How many cars pass through the intersection over the 30 minute period?
F(30) = 84cars/min

2. Is the traffic flow increasing or decreasing at t=7? Justify your answer.

Do I take the derivative and then plug in 7?

3. What is the average value of the traffic flow over the time interval 10<equal t <equal 15?

avg = 1/15-10 times the integral of f(t) from 10 to 15.
I tried to do this on the calculator but the f(t) function will not graph. What am i doing wrong? (TI-83 Plus)

Can someone help me/check my work? Thank you.[/code]

 

[stapel]

1) Since F(t) is defined to be "the flow per minute", then F(30) necessarily would provide only the cars going by in the thirtieth minute. To find the total number during the entire period, one would need to use a different process.

2) To find the change in the rate, yes, you would want to differentiate.

3) Since we cannot see your calculator or its various settings, nor can we see what you've entered into it, nor the results you obtained, I'm afraid there is little we can do in the way of trouble-shooting your hardware. Sorry.

Meanwhile, to answer the exercise, what have you learned about finding the average value of a function over an interval?

Eliz.

 

[paulxzt]

1) Since F(t) is defined to be "the flow per minute", then F(30) necessarily would provide only the cars going by in the thirtieth minute. To find the total number during the entire period, one would need to use a different process.

2) To find the change in the rate, yes, you would want to differentiate.

3) Since we cannot see your calculator or its various settings, nor can we see what you've entered into it, nor the results you obtained, I'm afraid there is little we can do in the way of trouble-shooting your hardware. Sorry.

Meanwhile, to answer the exercise, what have you learned about finding the average value of a function over an interval?

Eliz.

Ohh I would integrate it for 1) first?
Um the only thing I think you would need to know is I typed in 82 + 4sin(x/2) and tried to graph it. The windows setting was set to Z-standard.