Lastname: Firstname: Be certain to show all work manually on these sheets, scan and return for full credit. Math-2412.WS1 Due: Wed, Jun 14 Prof: Bock LAB #1 1a. A sheet of cardboard 3 ft by 8 ft is used to make an open box by cutting squares of equal size x from the corners and folding up the sides. Find a formula for V(x), the volume of this box. x x 1b. State the domain of V(x). 2. A ball is thrown upward from the top of a 160-ft building. If y(t) = 160 + 48t -16t is its equation of motion where t 0 is time (sec) and y(t) is altitude (ft) above the ground; also, the velocity of the ball is v(t) = 48 - 32t : a). when does the ball hit the ground (t = ?): b). the maximum height of the ball is y = ?: page 2 Math-2412.WS1 Due: Wed, Jun 14 Prof: Bock LAB #1 (cont'd) 3. Given p(x) = 2x - 3x + x - 30 and q(x) = x - 3, the quotient r(x) = p(x) q(x) = (p/q)(x) is: 4. a). If p(x) = 4x - 2x and q(x) = -2x + x + 1, r(x) = (p/q)(x) has what horizontal asymptote(s): b). If p(x) = x - 1 and q(x) = 3x - 12, r(x) = (p/q)(x) has what vertical asymptote(s) (even/odd): 5. x 3 3x 2 and label all intercepts and all asymptotes (state even or odd): Sketch r ( x) ( x 2) 2 ( x 3) page 3 Math-2412.WS1 Due: Wed, Jun 14 Prof: Bock LAB #1 (cont'd) 4 -1 , find (x) (if it exists): x3 6. Given (x) = 7. For the given function f ( x ) , evaluate f (8) f (2) : 4 x 10 x 2 f ( x) 5 8 x 24 / x x 4 3 x 4 4 x page 4 Math-2412.WS1 Due: Wed, Jun 14 Prof: Bock LAB #1 (cont'd) 1 x and g(x) = , the quantity g (simplified) is: x x 1 8. Given that the functions (x) = 9. Given that (x) = 1 + 2x , evaluate 10. Where is the function (x) = 2x + x - 6 negative? Graph this solution on the real number line. f (1 h) f (1) : h Math-2412.WS1 page 5 Due: Wed, Jun 14 Prof: Bock LAB #1 (cont'd) (11-14): Get exact answers for all real x & show work - no calculators: 11. 96 x 32 x 4 13. 23 x 0.52 x 2 2 12. ln( x 2 24) ln10 ln x 14. log x log x 1 log 5 25 x 1 x page 6 Math-2412.WS1 Due: Wed, Jun 14 Prof: Bock LAB #1 (cont'd) (15-18): Applications - set up equations and solve (calculator OK): 15. Through past observation, it has been determined that given enough food and space, the number of mice in a science lab will triple their current number after 18 weeks. To the nearest week, how long until the mice increase by 75% over their current number? 16. A bone is found in an ancient African cave and tested out at only 10% of its original amount of carbon-14. Estimate the age of the bone if the half-life of carbon-14 is about 5700 years. page 7 Math-2412.WS1 Due: Wed, Jun 14 Prof: Bock LAB #1 (cont'd) 17. How long does it take for $10,000 to become $17,500 if your money is placed in a CD that draws 4.5% compounded quarterly? Get answer in years and months (nearest month). 18. Assuming monthly compounding, in order to make a profit of $3850 on $10,000 in 5 years and 9 months, what is the annual percent interest rate necessary (within 0.01%)