Avalanche researchers know that the temperature gradients within a snowpack are highly responsive to air

temperature changes at the surface of the snowpack. These changing temperature profiles within the

snowpack can result in the structural failure of existing weak layers. The researchers have collected data

that measures the air temperature (in degrees Celsius) just above the snow surface over a period of 5 hours,

where t = 0 corresponds to noon on a particular day.

The air temperature function is given by

1

2

() =

(3 2)(2 5)

( 4)

for

t [0,5] hours

5

a)

In the data collection window, [0,5], when is the air temperature at freezing?

b)

In the data collection window, when is the air temperature above freezing (causing melt at the snow

surface)?

You will need to construct a sign chart to answer this question.

c)

Sketch the function on the interval [0,5], using the information obtained above.

d)

Confirm that the prediction by the LCT is consistent with your sign chart.

e)

Confirm that the prediction by the Multiplicity Test is consistent with your sign chart.