Chapter 8 - Section 8.4 - Plane Curves and Parametric Equations - 8.4 Exercises - Page 618: 45

(a) $x=2^{\frac{t}{12}}~cos~t$ $y=2^{\frac{t}{12}}~sin~t$ (b)

(a) $r=2^{\frac{θ}{12}}$ $x=r~cos~θ=2^{\frac{θ}{12}}~cos~θ$ $y=r~sin~θ=2^{\frac{θ}{12}}~sin~θ$ Change $θ$ by $t$: $x=2^{\frac{t}{12}}~cos~t$ $y=2^{\frac{t}{12}}~sin~t$