The amount of a radioactive substance decreases exponentially, with a decay constant of 3% per month. a. Write a differential equation to express the rate of change. b.Find a general solution to the differential equation from part a. c. If there are 75 g at the start of the decay process, find a particular solution for the differential equation from part a. d.Find the amount left after 10 months.

The following definitions and program segments has errors. Locate as many as you can. vector numbers = { 1, 2, 3, 4 };

To determine how fast a change in weight will occur, the most plausible assumption is that dw/dt is proportion to the net excess (or deficit) C-17.5w in the number of calories per day. a. Assume C is constant and write a differential equation to express this relationship. Use k to represent the constant of proportionality. What does C being constant imply? b.The units of dw/dt are pounds per day, and the units of C-17.5w are calories per day. What units must k have? c. Use the fact that 3500 calories is equivalent to 1 lb to rewrite the differential equation in part a. d.Solve the differential equation. e. Let $w_0$ represent the initial weight and use it to express the coefficient of $e^{-0.005 t}$ in terms of $w_0$ and C.

A recent report by the U.S. Census Bureau predicts that the U.S. Hispanic population will increase from 35.6 million in 2000 to 102.6 million in 2050. Assuming the unlimited growth model dy/dt=ky fits this population growth, express the population y as a function of the year t.Let 2000 correspond to t=0.

What is the difference between an argument and a parameter variable?

The half-life of palladium-100 is 4 days. After 20 days a sample has been reduced to a mass of 0.375 g. What was the initial mass of the sample?

Suppose the rate at which a rumor spreads - that is, the number of people who have heard the rumor over a period of time-increases with the number of people who have hear' it. If y is the number of people who have heard the rumor, then

$$\frac{d y}{d t}=k y$$

where t is the time in days. (a) If y is 1 when t=0, and y is 5 when t=2, find k. Using the value of k from part (a), find y for each time. (b) t=3 (c) t=5 (d) t=10

Decide whether the functions defined as follows are probability density functions on the indicated intervals. If not, tell why. $f(x)=2 x^{2}$; [-1, 1]

Find the matrix A of the quadratic form associated with the equation. $16 x^{2}-4 x y+20 y^{2}-72=0$

In your own words, define a random variable.

Subscript numbering in C++ always starts at _______.

Find the length of the curve correct to four decimal places. (Use a calculator to approximate the integral). r(t) = $\langle$ cos π t, 2t, sin 2πt$\rangle$, from (1, 0, 0) to (1, 4, 0)

The evapotranspiration index I is a measure of soil moisture. An article on 10- to 14-year-old heath vegetation described the rate of change of I with respect to W, the amount of water available, by the equation $\frac{d I}{d W}=0.088(2.4-I)$. a. According to the article, I has a value of 1 when W=0. SOlve the initial value problem. b.What happens to I as W becomes larger and larger?

An isolated fish population is limited to 4000 by the amount of food available. If there are now 320 fish and the population is growing with a growth constant of 2% a year, find the expected population at the end of 10 years.