This phenomenon is modeled with a differential equation, and that equation may be solved to give
T(t) = TA + [T0 − TA]b^t
where T(t) is the varying temperature of the object at a
given time, t, TA is the surrounding ambient temperature,
T0 is the initial temperature of the object, and b is a
constant that depends on the material the object is
composed of and how fast it heats or cools.
Suppose you decided to make a cup of hot tea
heated to 220 F in the kitchen that is at 70 F.
1.Solve the above equation for the constant b.
2.If the cup of hot tea cooled to 170 F in
10 minutes, find the value of the constant b in
the above equation. Express your answer to
5 decimal places.
3.Solve the above equation for t.
4.Suppose you like your hot tea at the tepid
temperature of 100 F. How long, to the nearest
minute, will you have to wait until it cools to this
temperature?
To go along with your hot tea, you take a frozen apple pie from
the freezer and place it in the oven preheated to 350 F. Assume the
freezer is at 32 F.
5.If the apple pie comes to a temperature of 100 F in
20 minutes, find the value of the constant b in the
above equation. Express your answer to 5 decimal
places.
6.How long will it take for the pie to reach its final
temperature of 200 F?
7. The pie is taken out of the oven and set on a table
in a room at 70 F. In 10 minutes, it has cooled to
180 F. However, the pie must cool to 120 F
before it is ready to eat. How much longer will
you have to wait?

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step-by-step explanation:

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

the results from a pre-test for students for the year 2000 and the year 2010 are illustrated in the box plot. what do these results tell us about how students performed on the 29 question pre-test for the two years?

if we compare only the lowest and highest scores between the two years, we might conclude that the students in 2010 did better than the students in 2010. this conclusion seems to follow since the lowest score of 8 in 2010 is greater in value than the lowest score of 6 in 2000. also, the highest score of 28 in 2010 is greater in value than the highest score of 27 in 2000.

but the box portion of the illustration gives us more detailed information. the middle bar in each box shows us that the median score of 20 in 2000 is greater in value than the median score of 17 in 2010. further, we note that the box and whiskers divide the illustration into four pieces. each of these four pieces represents the same portion of students. so, the upper half of the students in 2000 scored in the same score range as the upper one-fourth of the students in 2010, see the illustration at a score of 20.

by considering the upper one-fourth, upper half, and upper three-fourths instead of just the lowest and highest scores, we would conclude that the students as a whole did much better in 2000 than in 2010. we would conclude that as a whole the students in 2010 are less prepared than the students in 2000.

in this section, we discuss box-and-whisker plots and the five key values used in constructing a box-and-whisker plot. the key values are called a five-number summary, which consists of the minimum, first quartile, median, third quartile, and maximum.

step-by-step explanation: