Suggested languages for you:

Americas

Europe

Problem 10

Complete the given table with the values of the 3 -unit moving average of the given function. HINT [See Example 3.] $$ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline \boldsymbol{x} & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \boldsymbol{s}(\boldsymbol{x}) & 2 & 9 & 7 & 3 & 2 & 5 & 7 & 1 \\ \hline \bar{s}(\boldsymbol{x}) & & & & & & & & \\ \hline \end{array} $$

Expert verified

The 3-unit moving averages for the given function s(x) are:
$$
\begin{array}{|c|c|}
\hline \boldsymbol{x} & \bar{s}(\boldsymbol{x}) \\
\hline 1 & 6 \\
\hline 2 & 6.333 \\
\hline 3 & 4 \\
\hline 4 & 3.333 \\
\hline 5 & 4.667 \\
\hline 6 & 4.333 \\
\hline
\end{array}
$$

What do you think about this solution?

We value your feedback to improve our textbook solutions.

- Access over 3 million high quality textbook solutions
- Access our popular flashcard, quiz, mock-exam and notes features
- Access our smart AI features to upgrade your learning

Chapter 14

Variable Sales The value of your Chateau Petit Mont Blanc 1963 vintage burgundy is increasing continuously at an annual rate of \(40 \%\), and you have a supply of 1,000 bottles worth $$\$ 85$$ each at today's prices. In order to ensure a steady income, you have decided to sell your wine at a diminishing rate-starting at 500 bottles per year, and then decreasing this figure continuously at a fractional rate of \(100 \%\) per year. How much income (to the nearest dollar) can you expect to generate by this scheme? HINT [Use the formula for continuously compounded interest.]

Chapter 14

Profit Your monthly profit on sales of Avocado Ice Cream is rising at an instantaneous rate of \(10 \%\) per month. If you currently make a profit of $\$ 15,000$ per month, find the differential equation describing your change in profit, and solve it to predict your monthly profits. HINT [See Example 3.]

Chapter 14

Growth of Tumors The growth of tumors in animals can be modeled by the Gompertz equation: $$ \frac{d y}{d t}=-a y \ln \left(\frac{y}{b}\right) $$ where \(y\) is the size of a tumor, \(t\) is time, and \(a\) and \(b\) are constants that depend on the type of tumor and the units of measurement. a. Solve for \(y\) as a function of \(t\). b. If \(a=1, b=10\), and \(y(0)=5 \mathrm{~cm}^{3}\) (with \(t\) measured in days), find the specific solution and graph it.

Chapter 14

Meteor Impacts The frequency of meteor impacts on earth can be modeled by $$ n(k)=\frac{1}{5.6997 k^{1.081}} $$ where \(n(k)=N^{\prime}(k)\), and \(N(k)\) is the average number of meteors of energy less than or equal to \(k\) megatons that will hit the earth in one year. \({ }^{49}\) (A small nuclear bomb releases on the order of one megaton of energy.) a. How many meteors of energy at least \(k=0.2\) hit the earth each year? b. Investigate and interpret the integral \(\int_{0}^{1} n(k) d k\).

Chapter 14

Decide whether or not the given integral converges. If the integral converges, compute its value. $$\nabla_{-\infty}^{0} \frac{2 x}{x^{2}-1} d x$$

The first learning app that truly has everything you need to ace your exams in one place.

- Flashcards & Quizzes
- AI Study Assistant
- Smart Note-Taking
- Mock-Exams
- Study Planner