Chapter 11 Test

Question 1

Solve the following differential equation for the general solution:dy/dx=4x/3y+1.

Answer 1

3/2y^2+y=2x^2+C

Question 2

Solve the following differential equation for the general solution:2x−ydy/dx=3.

Answer 2

x^2−3x=1/2y^2+C

Question 3

Solve the following differential equation for the general solution: dy/dx=xy2

Answer 3

y=−2/x^2+C

Question 4

Find the particular solution to y dx = x dy given that y (8) = 2.

Answer 4

ln|x|=ln|y|+ln4

Question 5

Use Euler’s method with step size 0.5 to compute the approximate y-value y(2) of the solution of the initial-value problem y ′ = xy, y(0) = 1.

Answer 5

y(2) ≈ 3.28125

Question 6

A fruit fly population of 182 flies is in a closed container. The number of flies grows exponentially, reaching 340 in 18 days. Find the doubling time (time for the population to double) to the nearest tenth of a day.

Answer 6

20.0 days

Question 7

A sum is invested at 4% continuous interest. This means that its value grows exponentially with k equaling the decimal rate of interest. Find, to the nearest tenth of a year, the time required for the investment to double in value.

Answer 7

17.3 years

Question 8

Evaluate the following as true or false. In a problem dealing with exponential growth with a known doubling time, you may use any initial population P0 > 0 you wish when solving for k.

Answer 8

true

Question 9

A population grows exponentially, doubling in 4 hours. How long, to the nearest tenth of an hour, will it take the population to triple?

Answer 9

6.3 hours

Question 10

The half-life of iodine-126 (I 126 ) is 13 days. Of an original sample of 1,000.0 grams, how may grams of I 126 will remain after 98 days? Give the answer to the nearest tenth of a gram.

Answer 10

5.4 g

Question 11

While alive, an organism absorbs (radioactive) carbon 14 at such a rate that the proportion of carbon 14 in the organism remains at a known constant level. When it dies, it no longer absorbs carbon 14, so its proportion of carbon 14 begins to decrease. The half-life of carbon 14 is 5,600 years. A human skeleton is discovered whose level of carbon 14 is 15% that of a living human. To the nearest 100 years, how long ago did the person die?

Answer 11

15,300 years

Question 12

Which of the following is not a solution of d2y/dx2=3y?

Answer 12

y=sin√3x