\underline{Quiz 4}

Davis Name: M212 Pledge:

(9pts.) 1. A big oil company locates a vast oil reserve under the ocean. After 5 years of development, they expect to begin extracting oil at the rate of q(t) = 5 + t million barrels of oil per year (t is measured in years from discovery). If oil costs $20 per barrel, compute the present value of the oil that will be sold over the first 15 years of production.

(NOTE: USE 5% AS INTEREST RATE)

Present Value = ∫_{5}^{20}(5 + t)(20)e^{−.05t}dt = 20e^{−.05t}/(−.05)(5 + t + 20)|_{5}^{20} = 20(45e^{−1}/(−.05) − 30e^{−.25}/(−.05)) = 2723.8 million dollars.

(11pts.) 2. Match the slope fields with their differential equations. Then choose two of the differential equations to solve algebraically by separation of variables.

a. \frac{dy}{dx} = y + x^{2}y

y = e^{x+x^{3}/3+C}

b. \frac{dy}{dx} = xy^{2} sin (x^{2})

1/y = −1/2 cos (x^{2}) + C

c. \frac{dy}{dx} = y + xy

y = e^{x+x^{2}/2+C}

d. \frac{dy}{dx} = xe^{y}

−e^{−y} = x^{2}/2 + C

b. d.

a. c.