2. Find x e3x dx using integration by parts.
3. Let C(t) denote the concentration of a drug in blood stream, measured in mg/cm3 , t hours after an injection. Using the graph of C(t) below estimate the bioavailability of the drug over the 12-hour period following the injection. Give units with your answer.
6. Which of the following functions
(a) y = t2 (b) y = e2t
are solutions to the differential equation t dy/dy = 2y ? Explain your reasoning !
7. The length of a snake in inches, in an adult population of a certain species is normally distributed with mean 46 and standard deviation 2.
(a) Write a formula for the density of the distribution.
(b) Write the definite integral which represents the fraction of the population with the length between 44 and 48 inches. Without evaluating the integral, what do you expect it to be ? Why ?
8. The graph below gives the density function for the amount of time spent waiting for a bus at a bus stop.
(b) What fraction of people will wait less than an hour ? Between 1.5 and 2 hours ?
(c) In what half-hour interval is the waiting time most likely to fall ?
the median waiting time.
9. A possible model for the density function for the US age distribution is
(a) Write the definite integral which represents the mean age in the US.
(b) Evaluate the integral using the Fundamental Theorem of Calculus.
10. Find the cumulative distribution
function p(t) for
the age density in Problem 9. Explain its meaning.