1. kg m²/s²

2. x =; gives the zeroes of a quadratic function in terms of the coefficients

3. b, d

4. c

5. Constant half-life implies a decaying exponential; decay factor approximately 0.933;

y = C(0.933)^x, where C is the initial amount of material, x is the number of years, and y is the amount after x years

6. (a) t=4.78 (b) t=3

7. x=2, y=3 is the solution, which is the point of intersection of the two lines

8. (a) z³/(y⁴x²) (b) a¹⁴/(b⁶c¹⁰)

9. A vertical line placed anywhere in the x-y plane should cross the curve in no more than one point

10. Since 54 is between 49 and 64, its square root is between 7 and 8

11. After 3 iterations, estimates are: 6.96 and 3.31 (assumes first guesses are 23 and 1)

12. ln(30) = log₂(30)/log₂(e) = log₂(30)/log₂(2.718)

13. 3 db

14. pH = 5 is acidic; pH = 8 is basic; ratio of hydrogen ions = 1000

15. y = -2x + 7

16. No real zeros; y-intercept at -1.5; vertex at (1,-1); opens downward

17. 5.5% compounded annually is a better deal because the growth factor is larger (1.055 compared to 1.0513)

18. f(x) = x⁶ + 6x⁵ + 15x⁴ + 20x³+ 15x²+ 6x + 1; f(0)=1; f(-1)=0; f(9)=1M

19. y = (5/16)e^4.5x

20. (a) 1 (b) 4 (c) 1 (d) 2 (e) 4 (f) 3 (g) 3