Review:1. Solve for a: 43 = 2a

2. What is the domain for y = 2e-x - 3?

3. What is the range for y = tan x?

Answers:3. Domain:(-∞, ∞) Range: (-2,∞)6. 163x = (24)3x = 212x

9. x-intercept:≈-2.322 y-intercept: -3.012. x-intercept: 2.0 y-intercept:≈1.58515. c18. f21. Use 500,000(1.0375)t = 1,000,000 t ≈ 18.828

23.a. A(t) = 6.6(.5)t/14

b. t ≈ 38.114524. Use 2300(1.06)t = 4150 t ≈ 10.129

25. Use 2A = A(1.0625)t

2 = 1.0625t

t ≈ 11.433

26. Use A(1 + .0625/12)12t

t ≈ 11.119

27. Use 2A = Ae.0625t

t ≈ 11.090

32a. Use C(t) = 10,000(.8)t

t ≈ 10.319

b. t ≈ 41.275

36. x y ratio 1 8.155 2.718 2 22.167 2.718 3 60.257 2.718 4 160.79440a.y = 24121.49(1.0178)t

b. 36, 194,000 exceeds actual by 710,000 c. 1.8%

Parametric EquationsIf x and y are given as the functions x = f(t) y = g(t)over an interval of t-values, then the set of points (x,y) = (f(t),g(t)) defined by these equations is a parametric curve.

The equations are giving the horizontal and vertical positions over time.

t as a variable

Aside from setting our domain and range, we also need to set the interval of time we are looking at the equations.

What value of t should be our starting point?

Why would we want to have a negative value for the initial t?

Ex 1: Let x = a cos t and y = a sin t.a) Let a = 1, 2, or 3 and graph the parametric equations in a square viewing window using a parameter interval of [0,2π]. How does changing a affect the graph?

b) Let a = 2 and graph the interval over the following parameter values:[0,π/2]0,π][0,3π/2][0,2π][2π,4π][0,4π]Describe the role of the length of the parameter values.

Ex 2: Find the Cartesian equation for the parametric equationsa) x = t, y = 2t t ≥ 0

b) x = √t , t = t2 , t ≥0

Ex 3: Find the Cartesian equation for the parametric equationsa) x = 3 cost t, y = 3 sin t, 0 ≤ t ≤ 2π

b) x = 4 cos t, y = 2 sin t, 0 ≤ t ≤2π

Assignment: p 34 # 1-25 odd