1. A research lab grows a type of bacterium in culture in a circular region. The radius of the circle, measured in centimeters, is given by r(t)=5-6/(t^2+3) where t is time measured in hours passed since a circle of a 1cm radius of the bacterium was put into the culture. Express the area, A(t), of the bacteria as a function of time, and find the approximate area of the bacterial culture in 4 hours.
   1. A(t) =(56/(t2+3))andtheareaafter4hours=14.72cm2
   2. A(t) = 2(56/(t2+3))andtheareaafter4hours=29.43cm2
   3. A(t) =(56/(t2+3))2andtheareaafter4hours=68.93cm2
   4. A(t) =(56/(t2+3))2andtheareaafter4hours=137.86cm2

2. A minivan was purchased for $32,000. If the value of the minivan depreciates by $1,700 per year find a linear function that models the value V of the car after t years. Use the function and find the value of the car after 5 years

1. V(t) = -1,700 + 32000; value after 5 years = $23,500
2. V(t) = -1,700 + 32000; value after 5 years = $30,000
3. V(t) = -1,700 + 32000; value after 5 years = $33,700
4. V(t) = -1,700 + 32000; value after 5 years = $40,500

3. A Pendulum moving in simple harmonic motion is modeled by the function s(t)=5cos(/4) where s is measured in inches and t is measured in seconds. Determine the first time when the distance move is 4 inches.

1. .82s
2. 2.6s
3. 3.2s
4. 9.9s

4. Solve2log5(x)log5(6x1)=0

1. x = 1/6
2. x = 1/5
3. x = 5
4. x = 6

5. Estimate the slope of the tangent line tof(x)=x3 at x=2 by finding the slope of the secant line through (2, f(2)) and (2.001, f(2.001)).

1. 0.012
2. 4.02
3. 12.000
4. 16.0

6. Use the Squeeze theorem to evaluate limx0f(x) where f(x) =x2cos(3/x)

2. 0
3. 1

7. Find the intervals over which the function f(x)=2x2+3x+1/x25x

1. (,5)and5,)
2. (,0)and(0,)
3. (,0),(0,5)and(5,)
4. (,5),(5,0)and(0,)

8. find a non-zero value for the constant k that makes the function f(x)={tankx/x5x+3x<0x0}continuous at x = 0

1. -1/3
2. 1/3
3. 3
4. -3

9. A store determines the daily profit on pens. Obtained by charging s dollars per pen P(s)=10s2+75s5. If the store currently charges 50 cents for a pen. Find the rate of change of profits.

1. $30
2. $60
3. $65
4. $85

10. A ball is dropped from the top of a building that is 15m high. The position of the ball after t seconds is given by the equation s(t)=4.9t2+15. Find the instantaneous acceleration of the ball after t seconds.

1. 4.9m/s2
2. 9.8m/s2
3. 9.8tm/s2
4. 4.9tm/s2

11 Findd/dx(3/x2)+x(x1)

1. (3/x2)+2x1
2. (6/x3)+1
3. (3/x2)+1
4. (6/x3)+2x+1

12. The price p (in dollars) and the demand x for an item is given by the price-demand function p(x) = 15-0.0015x. Find the marginal revenue at x = 1,000.

1. $1.50
2. $12.00
3. $13.50
4. $15.00

13. A bag of sand hanging from a vertical spring is in simple harmonic motion as given by the position function s(t)=sin((/2)t+/6)where t is measured in seconds and s is in inches. Find the velocity of the spring at t = 2 s..

1. 3x/4
2. /4
3. 3x/4
4. /2

14 Find dy/dx ify=tan1(x3)

1. 1/1+x3
2. 1/2x3(1+x3)
3. 3x2/(1+x3)
4. 3x/2(1+x3)

15. The volume of a right cylinder of radius x and height y is given by v=x2y. Suppose that the volume of the cylinder is constant at 250cm3. find dy/dx when x = 5 and y = 10