A retail store estimates that weekly sales s and weekly advertising costs x (both in dollars) are related bys 80,000 30,000 e00020The current weekly advertisingcosts are $4,000, and these costs are increasing at a rate of $400 per week. Find the current rate of change of salesThe current rate of change of sales is $(Round to the nearest dollar as needed.)per weekEnter your answer in the answer box.hp

Question
Asked Oct 19, 2019
100 views
A retail store estimates that weekly sales s and weekly advertising costs x (both in dollars) are related bys 80,000 30,000 e00020The current weekly advertising
costs are $4,000, and these costs are increasing at a rate of $400 per week. Find the current rate of change of sales
The current rate of change of sales is $
(Round to the nearest dollar as needed.)
per week
Enter your answer in the answer box.
hp
help_outline

Image Transcriptionclose

A retail store estimates that weekly sales s and weekly advertising costs x (both in dollars) are related bys 80,000 30,000 e00020The current weekly advertising costs are $4,000, and these costs are increasing at a rate of $400 per week. Find the current rate of change of sales The current rate of change of sales is $ (Round to the nearest dollar as needed.) per week Enter your answer in the answer box. hp

fullscreen
check_circle

Expert Answer

Step 1

We differentiate the expression with respect to time, since time relation (i.e. week)  is mentioned in the question.

help_outline

Image Transcriptionclose

-0.00025x s 80000 3000 0e Differentiate with respect to t d d (80000-30000e000025 dt (s) dt d d (80000)(30000e -0.00025x dt dt dt d ds 0-30000 dt -0.00025x dt ds dx =-30000-(-0.0002 5x)(e0025). dt -0.00025x dt ds dx - 7.5 (e -0.00025x dt dt

fullscreen
Step 2

Substitute the giv...

help_outline

Image Transcriptionclose

ds dx - 7.5(e2 -0.00025x dt dt dx 400 Substitute x = 4000 dt ds -0.00025( 4000) 7.5(e - 400 dt ds 3000e dt ds = 1103.6 dt

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Derivative