Hospital patients are often given glucose (blood sugar) through a tube connected to a bottle suspended over their beds. Suppose that this “drip” supplies glucose at the rate of 25 mg per minute, and each minute 10% of the accumulated glucose is consumed by the body. Then the amount y(t) of glucose (in excess of the normal level) in the body after t minutes satisfies $y^{\prime}=25-0.1 y$ (Do you see why?) $y(0) = 0$ (zero excess glucose at t = 0) Solve this differential equation and initial condition.

A medical examiner called to the scene of a murder will usually take the temperature of the body. A corpse cools at a rate proportional to the difference between its temperature and the temperature of the room. If y(t) is the temperature (in degrees Fahrenheit) of the body t hours after the murder, and if the room temperature is 70$\degree$, then y satisfies

y' = -0.32(y - 70)

y(0) = 98.6 (body temperature initially 98.6$\degree$)

a. Solve this differential equation and initial condition.

b. Use your answer to part (a) to estimate how long ago the murder took place if the temperature of the body when it was discovered was 80$\degree$.

A cell stimulated to increase its steroid production will have abundant a. ribosomes b. rough ER. c. smooth ER d. Golgi apparatus e. secretory vesicles

For each demand function d(x) and demand level x, find the consumers’ surplus. $d(x)=300 e^{-0.2 \sqrt{x}}, \ x=120$

Use a graphing calculator to estimate the improper integrals $\int_{0}^{\infty} \frac{1}{x^{2}+1} d x$ and $\int_{0}^{\infty} \frac{1}{\sqrt{x}+1} d x$ (if they converge) as follows: a. Define $y_1$ to be the definite integral (using FnInt) of $\frac{1}{x^{2}+1}$ from 0 to x. b. Define $y_2$ to be the definite integral of $\frac{1}{\sqrt{x}+1}$ from 0 to x. c. $y_1$ and $y_2$ then give the areas under these curves out to any number x. Make a TABLE of values of $y_1$ and $y_2$ for x-values such as 1, 10, 100, 500, and 10,000. Which integral converges (and to what number, approximated to five decimal places) and which diverges?

List two factors that keep bones healthy. List two Factors that can cause bones to become soft or to atrophy.

Which parts of the thoracic vertebrae articulate with the ribs? a. Spinous process b. Transverse process c. Superior articular processes d. Body e. Pedicles

Random collections of nine different solutions of a calcium compound were given to two laboratories A and B. Each laboratory measured the calcium content (in mmol. per liter) and reported the results. The data are paired by calcium compound.

$$\scriptstyle\begin{array}{l|ccccccccc} \hline \text { Compound } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline \text { Lab A } & 13.33 & 15.79 & 14.78 & 11.29 & 12.59 & 9.65 & 8.69 & 10.06 & 11.58 \\ \hline \text { Lab B } & 13.17 & 15.72 & 14.66 & 11.47 & 12.65 & 9.60 & 8.75 & 10.25 & 11.56 \\ \hline \end{array}$$

Use a 5% level of significance to test for a monotone relation (either way) between ranks. Interpret the results.

Which of the following organ systems digestive, respiratory, reproductive, circulatory, urinary, or muscular are found in both subdivisions of the ventral body cavity? Which are found in the thoracic cavity only? In the abdominopelvic cavity only?

According to an article in Science News, binge eating has been associated with a mutation of the gene for a brain protein called melanocortin 4 receptor (MC4R). In one study, F. Horber of the Hirslanden Clinic in Zurich and his colleagues genetically analyzed the blood of 469 obese people and found that 24 carried a mutated MC4R gene. Suppose that you want to estimate the proportion of all obese people who carry a mutated MC4R gene. a. Determine the margin of error for a 90% confidence interval. b. Without doing any calculations, indicate whether the margin of error is larger or smaller for a 95% confidence interval. Explain your answer.

In playing a game, Tosha won 8 times, Pete won 7 times, and Maurice won 10 times. Based on this information, how many times would you expect Maurice to win if they play the game 100 times?

Use NDERIV to “find” the derivative of each function at x = 0. Is the result correct? $f(x)=\frac{1}{x^{2}}$

Reread, if necessary, the Application Preview. a. Evaluate the definite integrals $\int_{0}^{1}\left(300 e^{0.025 x}-240 e^{0.02 x}\right) d x$ and $\int_{7}^{8}\left(300 e^{0.025 x}-240 e^{0.02 x}\right) d x$ to verify the answers given there for the amount of tar inhaled from the first and last centimeters of the cigarette. b. Evaluate the definite integral $\int_{0}^{8}\left(300 e^{0.025 x}-240 e^{0.02 x}\right) d x$ to find the amount of tar inhaled from smoking the entire cigarette.

A 500-page book contains 250 sheets of paper. The thickness of the paper used to manufacture the book has mean 0.08 mm and standard deviation 0.01 mm. a. What is the probability that a randomly chosen book is more than 20.2 mm thick (not including the covers)? b. What is the 10th percentile of book thicknesses? c. Someone wants to know the probability that a randomly chosen page is more than 0.1 mm thick. Is enough information given to compute this probability? If so, compute the probability. If not, explain why not.