Question

The depth d (in feet) of a manmade lake is represented by the function d(t)= |2t-8|+13 where t is the month with t = 1 corresponding to January. What is the lowest depth of the lake?

a.) 21 ft
b.) 8ft
c.) 2 ft
d.) 13 ft

Answer 1

The minimum depth of the lake, based on the function d(t) = |2t-8| + 13, occurs at t = 4 months and is 13 feet.

Step-by-step explanation:

The lowest depth of the manmade lake is represented by the function d(t) = |2t-8| + 13, where t is the month.

To find the minimum depth, we need to consider the absolute value function inside d(t). The absolute value function reaches its minimum when the inside expression is 0. That happens when 2t - 8 = 0, so t = 4 months. Upon substituting t = 4 into the function we get d(4) = |2(4) - 8| + 13 = |0| + 13 = 13 feet. Therefore, the lowest depth of the lake is 13 feet.