1.) Sales of a particular product have been declining continuously at a rate of 8% each year. a. Express the rate of sales decline as a differential equation. b. Find the general solution for the equation in part (a). c. How long will it take sales to decrease by 6% from their original level?
1.) Sales of a particular product have been declining continuously at a rate of 8% each year.
a. Express the rate of sales decline as a differential equation.
b. Find the general solution for the equation in part (a).
c. How long will it take sales to decrease by 6% from their original level?
2. Let ?(?) be a function representing how many people in a certain city are “x” years old.
a. Interpret the expression ?(45) = 1000. Hint: this is telling us that x=45 and f(x)=1000.
Your answer should include the values 45 and 1000, and it should tell me what they
mean in terms of years and number of people.
b. Interpret the expression (expression in PICTURE below). Answer should include the values 32, 45, and 10,000, and it should tell me what they mean in terms of years and number of people.
c. If ?′(45) > 0, does that mean there are more or less people who are 46 than who are
45?
3. The graph below gives the marginal profit P′(?)for a company when it produces x products.
(Graph in PICTURE below)
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