Answer:
decrease of 1.153 sales per day
Step-by-step explanation:
Given:-
- The price of item = p
- The number of sales = x
- The relationship between "p" and "x" is given below:
5p+5x+3px=71
Find:-
Find the rate at which x is changing when x=3, p=4, and dp/dt=1.4. The rate at which x is changing is [ ] sales per day
Solution:-
- Take the time derivative (d/dt) of the entire given expression and apply chain rule on d/dt ( 3px ). Since both "p" and "x" are only functions of time "t":
d/dt (5p+5x+3px=71)
5*dp/dt + 5*dx/dt + 3* ( x*dp/dt + p*dx/dt) = 0
- Use the given values x=3, p=4, and dp/dt=1.4 to determine dx/dt:
5*1.4 + 5*dx/dt + 3*3*1.4 + 3*4*dx/dt = 0
17dx/dt = -19.6
dx/dt = -1.153 sales per day
- There is a decrease of 1.153 sales per day.
