Question 2 (Essay Worth 30 points) (04.05, 05.04, 07.04 HC)
At the start of the workday, 35,000 cubic feet of dirt was piled up at a construction site. Dirt will be added to the pile for the next 8 hours, satisfying the increasing
dP
differential equation
from the start of the workday.
(P-7,000), where the function Prepresents the total amount of dirt in the pile. Pis measured in cubic feet, and t is measured in hours
at
Part A: Estimate the amount of dirt in the pile after 3 hours, using the tangent line to the graph of Patt = 0. (10 points)
Part B: Find and used to determind or what you found in Part A was an underestimate or an overestimate at t = 3. (10 points)
dt2
dp
Part C: Find the general solution to the differential equation
(P-7.
(P-7,000). (10 points)