Chapter 7- Learning Outcome 1_Mathematics for Technologists
- 1. 21st Century Mathematics for the Industrial Technology Learners: Automotive Technology BABY 'RLENE I. BAYOC
- 2. Exponential and Logarithmic Functions and Complex Numbers Chapter VII 21st Century Mathematics for the Industrial Technology Learners: Automotive Technology
- 3. CHAPTER VII: Exponential and Logarithmic Functions and Complex Numbers Learning Outcome 1: Defined and discussed Exponential and Logarithmic Functions and apply the laws to solve real life problems..;
- 4. CHAPTER VII: Exponential and Logarithmic Functions and Complex Numbers
- 5. CHAPTER VII: Exponential and Logarithmic Functions and Complex Numbers
- 6. CHAPTER VII: Exponential and Logarithmic Functions and Complex Numbers In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, which must be raised, to produce that number x. In the simplest case, the logarithm counts the number of occurrences of the same factor in repeated multiplication; for example, 1000 = 10 × 10 × 10 = 103 , the "logarithm base 10" of 1000 is 3, or log10(1000) = 3. The logarithm of x to base b is denoted as logb (x).
- 7. CHAPTER VII: Exponential and Logarithmic Functions and Complex Numbers
- 8. CHAPTER VII: Exponential and Logarithmic Functions and Complex Numbers
- 9. CHAPTER VII: Exponential and Logarithmic Functions and Complex Numbers Some applications of exponential function: 1. In the absence of factors affecting population growth, the population after n years at a constant rate r is P(1 + r)n . If the population P is decreasing at a constant rate r, at the end of n years the population would be P(1 – r)n .
- 10. CHAPTER VII: Exponential and Logarithmic Functions and Complex Numbers 2. The half-life is the time it takes for half of a radioactive element to decay. To find the amount Pn of the radioactive substance with half-life k in n period of time, the formula to be used is Pn = P(1/2)n/k . The unit of k and n must be the same. 3. Compound interest behaves exponentially. This is explained by its formula A = P( 1 + r/m)tm where A is the total amount after t years of investing the principal amount P at r interest rate which is compounded m times a year.
- 11. CHAPTER VII: Exponential and Logarithmic Functions and Complex Numbers REFERENCE
- 12. CHAPTER VII: Exponential and Logarithmic Functions and Complex Numbers Thank you