Calculus homework

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QUESTION 1

1. Find the particular solution determined by the given condition. f'(x) = 3x2 - 2x; f(0) = 18

		f(x) = 3x3 + 2x2 + 18
		f(x) = 3x3 + x2 + 18
		f(x) = x3 - x2 + 18
		f(x) = x3 + 2x2 + 18

5 points

QUESTION 2

1. Find the general solution for the differential equation. y ' = 2e3x

		2e3x + C
		6e3x + C
		$C:\Users\joohn\Desktop\f1q4g2.jpg$ e3x + C
		$C:\Users\joohn\Desktop\f1q4g1.jpg$ e3x + C

5 points

QUESTION 3

1. Solve the problem. If a population is changed by either immigration or emigration, a model for the population is $C:\Users\joohn\Desktop\f1q19g1.jpg$ where y is the population at time t and f(t) is some function of t that describes the net effect of the emigration/immigration. Assume that k = 0.02 and y(0) = 10,000. Solve this differential equation for y, given that $C:\Users\joohn\Desktop\f1q19g2.jpg$

		y = 100t + 5000 + 5000e-0.02t
		y = 100t + 5000 + 5000e0.02t
		y = -100t + 5000 + 5000e-0.02t
		y = -100t - 5000 + 5000e0.02t

5 points

QUESTION 4

1. Solve the problem. The logistic differential equation $C:\Users\joohn\Desktop\f1q13g1.jpg$ = 0.08P(300 - P) describes the growth of a population P, where t is measured in years. Find the limiting population.

		600
		150
		2.4
		300

5 points

QUESTION 5

		y = 1100t - 55,000 + 65,000e-0.02t
		y = -1100t - 55,000 + 65,000e0.02t
		y = 1100t + 55,000 + 65,000e-0.02t
		y = -1100t - 55,000 + 65,000e-0.02t

5 points

QUESTION 6

1. Solve. $C:\Users\joohn\Desktop\f1q8g1.jpg$ = 8x7y

		y = Cex8
		y = 8Cx7ex7
		y = 8Cx8ex7
		y = 8Cx8ex8

5 points

QUESTION 7

1. Solve. $C:\Users\joohn\Desktop\f1q10g1.jpg$ = $C:\Users\joohn\Desktop\f1q10g2.jpg$

		y = ± $C:\Users\joohn\Desktop\f1q10g6.jpg$
		y = $C:\Users\joohn\Desktop\f1q10g4.jpg$ x + C
		y = $C:\Users\joohn\Desktop\f1q10g5.jpg$ x + C
		y = ± $C:\Users\joohn\Desktop\f1q10g3.jpg$

5 points

QUESTION 8

1. Find the general solution of the differential equation, or the particular solution if an initial condition is given. 5y' - 10xy - x = 0

		y = $C:\Users\joohn\Desktop\f1q17g1.jpg$ + Ce-x2/2
		y = - $C:\Users\joohn\Desktop\f1q17g1.jpg$ + Cex2
		y = - $C:\Users\joohn\Desktop\f1q17g1.jpg$ + Ce-x2
		y = - $C:\Users\joohn\Desktop\f1q17g1.jpg$ + Cex2/2

5 points

QUESTION 9

1. Find the general solution of the differential equation, or the particular solution if an initial condition is given. y' + 2y = 21

		y = $C:\Users\joohn\Desktop\f1q14g1.jpg$ + Ce2x
		y = 21 + Ce2x
		y = $C:\Users\joohn\Desktop\f1q14g3.jpg$ + e2x + Ce-2x
		y = $C:\Users\joohn\Desktop\f1q14g3.jpg$ + Ce-2x

5 points

QUESTION 10

1. Solve the problem. The logistic differential equation $C:\Users\joohn\Desktop\f1q20g1.jpg$ = 0.07P(700 - P) describes the growth of a population P, where t is measured in years. Find the limiting population.

		700
		4.9
		350
		1400

5 points

QUESTION 11

1. Find the particular solution determined by the given condition. y' = 4x + 10; y = -21 when x = 0

		y = 2x2 + 10x - 10.5
		y = 4x2 + 10x - 10.5
		y = 2x2 + 10x - 21
		y = 4x2 + 10x - 21

5 points

QUESTION 12

1. Find the general solution for the differential equation. y ' = 18x2

		x3 + C
		$C:\Users\joohn\Desktop\f1q1g1.jpg$ + C
		6x3 + C
		18x3 + C

5 points

QUESTION 13

1. Solve the problem. The growth rate of a certain stock is modeled by $C:\Users\joohn\Desktop\f1q11g1.jpg$ where V = the value of the stock, per share, after time t (in months), and k = a constant. Find the solution to the differential equation in terms of t and k.

		V = 39 - 39e-kt
		V = 29 - 10e-kt
		V = 39 - 10ekt
		V = 39 - 10e-kt

5 points

QUESTION 14

1. Find the general solution of the differential equation, or the particular solution if an initial condition is given. y' + 3y = 12

		y = 4 + Ce-12x
		y = 4 + Ce-3x
		y = $C:\Users\joohn\Desktop\f1q15g1.jpg$ + Ce3x
		y = 12 + Ce-3x

5 points

QUESTION 15

1. Find the general solution of the differential equation, or the particular solution if an initial condition is given. y' + 2xy = 21x

		y = $C:\Users\joohn\Desktop\f1q16g3.jpg$ + Ce-x2
		y = 21 + Cex2
		y = $C:\Users\joohn\Desktop\f1q16g3.jpg$ + 2x + Ce-x2
		y = $C:\Users\joohn\Desktop\f1q16g2.jpg$ + Cex2

5 points

QUESTION 16

1. Find the general solution for the differential equation. y ' = x - 16

		2x2 - 16 + C
		$C:\Users\joohn\Desktop\f1q2g1.jpg$ - x + C
		x3 - 16x + C
		$C:\Users\joohn\Desktop\f1q2g1.jpg$ - 16x + C

5 points

QUESTION 17

1. Solve the problem. Find the demand function q = D(x), given that E(x) = $C:\Users\joohn\Desktop\f1q12g1.jpg$ and q = e when x = 8.

		q = e8/x
		q = 8 lnx
		q = ln $C:\Users\joohn\Desktop\f1q12g2.jpg$
		q = $C:\Users\joohn\Desktop\f1q12g3.jpg$

5 points

QUESTION 18

1. Find the general solution for the differential equation. y ' = 72x2 - 20x

		72x3 - 10x2 + C
		72x3 - 20x2 + C
		24x3 - 20x2 + C
		24x3 - 10x2 + C

5 points

QUESTION 19

1. Find the particular solution determined by the given condition. y' = $C:\Users\joohn\Desktop\f1q6g1.jpg$ ; y = 21 when x = 1

		y = 5 ln x + 21
		y = ln x + 21
		y = ln x + 19
		y = 5 ln x + 2.5

5 points

QUESTION 20

1. Solve. 3y2 $C:\Users\joohn\Desktop\f1q9g1.jpg$ = 7x

		y = - $C:\Users\joohn\Desktop\f1q9g2.jpg$
		y = $C:\Users\joohn\Desktop\f1q9g4.jpg$
		y = - $C:\Users\joohn\Desktop\f1q9g5.jpg$
		y = $C:\Users\joohn\Desktop\f1q9g3.jpg$

5 points