Chapter 11 Test Flashcards Preview

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Flashcards in Chapter 11 Test Deck (12):
1

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

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

2

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

x^2−3x=1/2y^2+C

3

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

y=−2/x^2+C

4

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

ln|x|=ln|y|+ln4

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.

y(2) ≈ 3.28125

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.

20.0 days

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.

17.3 years

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.

true

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?

6.3 hours

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.

5.4 g

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?

15,300 years

12

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

y=sin√3x

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