Question

A roast turkey is taken from an oven when its temperature has reached 185°F and is placed on a table in a room where the temperature is 75°F. The graph shows how the temperature of the turkey decreases and eventually approaches room temperature. By measuring the slope of the tangent, estimate the rate of change of the temperature after an hour.

Answer 1

We'll have to see the chart.

Answer 2

That's it. We do have to get used to the scale of this chart. It's a little irregular.

Vertical lines are 50º apart.
Horizontal lines are 30 minutes apart.

Can you estimate the Temperature where the tangent lines crosses the 30 minute mark and the 90 minute mark?

Answer 3

That is what is hard for me. I would estimate it to be about 148 when it crosses the 30 min mark and then 102 for the 90 minute mark. Everything is just so abstract..

Answer 4

Agreed. Just a chart is NOT an exact science. You just have to get a feel for it.

1) Some folks would suggest that you cannot estimate more than one significant figure. In other words, you may not say 148, you must say 150 or 140. I think it';s a little silly, but it may come up at some point, so I thought I'd mention it.

2) Perfect. So, how much did the temperature change in the hour from 30 min to 90 min?

Answer 5

50 degrees if we round and 46 if we don't

Answer 6

I think we just estimated the rate of change after an hour. :-)

Answer 7

it would be negative correct?

Answer 8

That's right. We can eyeball it right around 60 minutes, but it is usually far more accurate to use surrounding data. In this case the most useful surrounding data were exactly one hour apart.

Notice that at 30 minutes the slope is a little more than 50 (negative) and at 90 minutes a little less than 50 (negative). Thus, it's not unreasonable to say that the slope is about 50 AT 1 hour.

Answer 9

Thank you so much! The homework said -50/60 is correct!

Answer 10

woo-hoo!!!