11. An international agency determines that the number of endangered species that remain in the wild t years after a protection policy is instituted is given by 600 N(t) = - 1+ 3e-0.02t At what rate is the population changing in 4 years? 12. A tiny spherical balloon is inserted into a clogged artery and is inflated at the rate of 0.002x cubic millimeters per minute. How fast is the radius of the balloon growing when the radius is 0.005 millimeters |V = > mr 3 13. A 26-foot ladder is placed against a wall. If the top of the ladder is sliding down the wall at a rate of 2 feet per second, at what rate is the bottom of the ladder moving away from the wall when the bottom of the ladder is 10 feet from the wall? 14. A particle oscillates so that its position varies according to the expression s(1)=4cos/ 21+ - where s(t) is in centimeters and t is in seconds. Find the particle's acceleration when t =0. 15. A person is flying a kite in a wind that is blowing east at a rate of 50 feet per minute. She has already let out 200 feet of string, and the kite is flying 100 feet above the ground. How fast must she let out string at this moment to keep the kite flying with the same speed and altitude? 16. Find the equation of the line tangent to the curve x y - 2xy = 6x + y +1 at the point (0, -1).ANSWERS 1. h'(t) = 7(+2 -303t ) (21 -90 3t ) 2. y = 5 COIN 27 3. 1.32 mg/meter per hour 4. a. dy cosx - 2y b. dy 2y2e2x dx 2x + siny -1 dx 1-ve 2x 5. f' ( x ) =- 3sinx - 2 3 6. s'(t) = (-3+2sinx)2 2(3t -1) 7. -0.55 liters per second 8. s'(r) =60r2(3r - 2)4 + 8r(3r -2)5 WIN mile per day; After 2 days, the radius of the oil slick is increasing by - miles/day. 10. y =~x+ 11. 2.34 species per year 12. 20 millimeters per minute 13. 4.8 feet per second 14. -11.314 cm/s2 15. 43.3 feet per minute 16. y =-4x-1