Question

PLEASE HELP 1) A lake near the Arctic Circle is covered by a 2-meter-thick sheet of ice during the cold winter

months. When spring arrives, the warm air gradually melts the ice, causing its thickness to
decrease at a constant rate modeled by h(t) = 2 - 0.25t, where h(t) represents the thickness of
the sheet of ice and t represents the time in weeks.
a. What is the initial value of this function?

b. What is the rate at which the ice sheet is melting?

c. How thick will the ice sheet be after 3 weeks?

Answer 1

a). 2 meters

b). 0.25 meters per week

c). 1.25 meters

Explanation:

Thickness of the ice sheet on the lake = 2 meters

Thickness decreases with a constant rate and thickness is modeled by the function,

h(t) = 2 - 0.25t [t = time or duration in weeks]

a). Initial value of this function will be it's y-intercept,

h(t) = 2 meters

b). Rate of the melting of this sheet (slope of the line) = 0.25 meter per week

c). After 3 weeks or t = 3 weeks,

h(3) = 2 - 0.25 × (3)

= 2 - 0.75

= 1.25 meters