For #1-9, suppose a ball's heights in feet at time t in seconds is given by s(t) = 64 - 16(t− 1)² 1. Sketch a graph of y = s(t) on the time interval [0,3]. Label the points on the graph that correspond to when the ball is released, when it reaches its highest point, and when it lands. 2. How does the ball's motion differ on the time intervals (0, 1) and (1,3)? What occurs at the instant t = 1? 3. Compute the ball's average velocity on the following time intervals. Include units for each. (a) [0.4, 0.8] (e) [0.8, 1.2] (b) [0.7,0.8] (c) [0.79,0.8] (d) [0.799,0.8] (f) [0.8,0.9] (g) [0.8, 0.81] (h) [0.8,0.801]

The U.S. population can be modeled by the function y=165.6x¹.345, where y is in thousands and x is the number of years after 1800. (a) What was the population in 1970, according to this model? (b) is the graph of this function concave up or concave down? What does this mean? (c) Use numerical or graphical methods to find when the model estimates the population was 94,150,000. (a) According to the model, the population in 1970 was thousands. (Round to the nearest integer as needed.)

Sarah pays a flat rate plus a rate per minute for her phone plan as shown in the graph above. The cost of Sarah's phone plan, C(t), can be represented by which of the following functions? A: C(t) = -0.10t+25 B: C(t) = 0.10t+25 C: C(t) = 25(0.10)^t D: C(t) = 25(1+0.10)^t

2. Given g(x) =- ft(* - 3)) – 5where f(x) = 2" a. Write the equation of the transformed function b. Graph the transformed function. Be sure to show all steps! c. State the domain ana range of the function -10