Sections: 1.3 and 1.5 m > 0 Positive Rising, Increasing Concave up Use the following table to decide if the function is increasing, decreasing, concave up, concave down: f(t) = 3 5 10 18 30 f(t) = 3 10 15 18 20 a) The values are increasing, then the function is increasing or rising. Slope of the tangent line > 0 a) The values are increasing, then the function is increasing or rising. Slope of the tangent line > 0 b) from 3 to 5: increases by 2 from 5 to 10: increases by 5 from 10 to 18: increases by 8 from 18 to 30: increases by 12 It increases in faster and faster rate, then it is Concave Up b) from 3 to 10: increases by 7 from 10 to 15: increases by 5 from 15 to 18: increases by 3 from 18 to 20: increases by 2 It increases in slower and slower rate, then it is Concave Down m > 0 Positive Rising, Increasing Concave down m > 0 Positive Rising, Increasing Concave up

Concave up, Concave down, Increasing, Decreasing Use the following table to decide if the function is increasing, decreasing, concave up, concave down: (notice that the tables are the same as the previous example, but in reverse order) f(t) = 30 18 10 5 2 f(t) = 20 18 15 10 3 a) The values are decreasing, then the function is decreasing or falling. Slope of the tangent line < 0 a) The values are decreasing, then the function is decreasing or falling. Slope of the tangent line < 0 b) from 30 to 18: decreases by 12 from 18 to 10: decreases by 8 from 10 to 5: decreases by 5 from 5 to 2: decreases by 3 It decreases in slower and slower rate, then it is Concave Up b) from 20 to 18: decreases by 2 from 18 to 15: decreases by 3 from 15 to 10: decreases by 5 from 10 to 3: decreases by 7 It decreases in faster and faster rate, then it is Concave Down Concave up m < 0 Negative Falling, Decreasing m < 0 Negative Falling, Decreasing Concave down

Linear Increase or Decrease Exponential Growth or Decay f(t) t 1 2 3 4 6 8 10 12 Linear Increase y = mx + b m > 0 f(t) t 2 4 6 8 12 9 3 Linear Decrease y = mx + b m < 0 Or: y = 2x + 4 ; (m = 2) Or: y = -1.5x + 12 ; (m = -1.5) f(t) t 1 2 3 12 13.2 14.52 15.972 f(t) t 1 2 3 15 12 9.6 7.68 Exponential Growth P=P0(a)t a > 1 Exponential Decay P=P0(a)t a < 1 Or: P = 12(1.1)t ; (a = 1.1) Or: P = 15(0.8)t ; (a = 0.8)