retail store estimates that weekly sales s and weekly advertising costs x both in dollars are related by s=40,000-30000e^-0.00025x. The current weekly advertising cost are $4,000 and these costs are increasing at a rate of $400 per week. Find the current rate of change of sales

Q: Suppose the income from an Internet access business is a continuous income stream with annual rate…

A: We have given the rate of annual flow,f(t)=900 t e-0.1t

Q: The price of 1 gallon of unleaded gasoline at the pump dropped to $2.19 on January 1, 2015, and…

A: As the price of  1 gallon of unleaded gasoline is decreasing  4 cents per month starting from…

Q: The worst ecological disaster in U.S. history began on April 20, 2010, and was caused by an…

A: bn=2.520n & rn=441,000n a). an=bn-rn=2.520n-441,000n=-4,40,997.48n

Q: home owner installs a solar heating system, which is expected to generate savings at the rate of…

A: Given query is to find the formula for total savings in t year.

Q: uppose another drug is administered intravenously. The concentration c

A:

Q: The population of beetles is growing at a rate of 5% each month.  The current population is 800.…

A: Given that the population of beetles is growing at a rate of 5% each month and the current…

Q: The rate of residential electricity consumption (in billions of kilowatt hours (kWh) per year) of a…

A:

Q: average cost per gigabyte of RAM can be approximated by the function C(t)= 8,500,000(0.65)^ t, where…

A: Given query is to find the the average cost of ram for the given time.

Q: In order to save up for Post Secondary, Narissa’s parents invested $4500.00. Their money earns…

A: Given, A0= $ 4500 k= 2 r=8%= 8/100= 0.08 t= 5 years

Q: The value, v of a computer is modeled by the function V(t)=500(0.82)^t where t is the number of…

A: The value of computer is modeled by the function,  V(t) = 500(0.82)t Where t is time in years

Q: N(t)= 250,000(.494)^t When will 10 percent of the original amount of aluminum be in use? In years

A: The given equation is: Nt=250,0000.494t To find: When will 10 percent of the original amount of…

Q: In a given community, the number of thousands of people infected with a strain of flu t weeks after…

A:

Q: Describe the relationship of input and output values for composite functions

A: Use the definition of composition of two functions.

Q: The worst ecological disaster in U.S. history began on April 20, 2010, and was caused by an…

A: The function bn is given by:                      bn=2.520n million gallons where, bn represents the…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.