Question

The surface temperature of a deep, spring-fed lake is 70F. The lake temperature drops 2F for each yard below the lake surface until a depth of 6 yards is reached. From 6 yards to 15 yards deep, the temperature is constant. From 15 yards down to the spring source, the temperature increases 3F per foot until the spring source is reached at 2 yards below the surface.

a. What is the temperature at 10 yards below the surface?

b. What is the temperature at 50 feet below the surface?

c. Write an expression

Answer 1

a. At the end of 6 yards, the temperature drops to 70 - 5(2) = 70 - 10

= 60 F

Since from 6 yards to 15 yards, the temperature is constant, the temperature at 10 yards below the surface is 60F.

b. 50 feet is approximately 17 yards.

Since the temperature increases 3F per foot after 15 yards,

Increase in temperature after 15 yards = 17 - 14 = 3 yards

= 3(3) = 9 feet

The temperature at 50 feet below the surface = 60 + 3(9)

= 87 F

c. Please check the expression in the image attached.

Since 1 yard = 3 feet, and the temperature increases 3F per foot, from 15 yards,

the temperature = 60 + (t - 14)(3)(3)

= 60 + 9(t - 14)

= 60 + 9t - 126

= 9t - 66