QUESTION

On a certain day at a diner, the total number of food orders taken by time t is modeled by the function F that satisfies the differential equation dF/dT= 48/(√3t+1) with F(1)=32, where t is the number of hours since the diner opened and 0≤t≤8.

(a) Write an equation for the line tangent to the graph of F at t=1. Use this equation to approximate the total number of food orders taken by time t=2.

(b) Find F′′(5). Using correct units, interpret the meaning of F′′(5) in the context of the problem.

(c) Find an expression for F(t). Based on this model, what is the total number of food orders taken by time t=8 ?

Public Answer

VDJWFT The First Answerer