Year 12/AS Pure Chapter 14.2 (Exponentials and Logarithms)

This video formally introduces the important mathematical constant e and its properties and definitions. Next, we have a look at differentiating functions of the type y = eˣ, y = eᵏˣ and even (beyond the scope of the suggested exercise) y = eᵏˣ⁺ᵇ. The lesson concludes by sketching graphs of the type y = a + beᵏˣ. This lesson is meant as preparation for Exercise 14B, page 316 of the Pearson Edexcel Pure Mathematics Year 1/AS Textbook: bit.ly/PuretextbookYear1 #exponentials #logarithms #9MA0 Introduction: 00:00 Solution to Warm-Up Q1: 0:44 Solution to Warm-Up Q2: 3:15 Solution to Warm-Up Q3: 4:45 Solution to Warm-Up Q4: 7:02 The constant e - approximate value and formal definitions: 12:41 The constant e - key properties: 14:04 WORKED EXAMPLES - DIFFERENTIATING eᵏˣ: 14:59 Worked Example 1a: 15:00 Worked Example 1b: 15:29 Worked Example 1c: 15:54 Worked Example 2: Differentiating y = eᵏˣ⁺ᵇ: 16:32 WORKED EXAMPLES - SKETCHING GRAPHS OF EXPONENTIAL FUNCTIONS: 21:53 Sketch a: 22:15 Sketch b: 25:20 Sketch c: 28:14 Suggested Exercises: 30:58