MHF4U - Unit 6 - Exponential and Logarithmic Functions

Lesson 1 - The Exponential Function and It’s Inverse

• Exponential Function - A function of the form y = a^x, where a > 0, and a ≠ 1

  • The graph of y = a^x will pass through the point (0,1)

• Exponential Growth - y = ka^x, k > 0, a > 1

• Exponential Decay - y = ka^x, k > 0, 0 < a < 1

• Half Life

  • A(t) = A_o(1/2)^t/h

  • A(t) is the amount at a given time

  • A_o is the original amount

  • t is the time that has passed, in the same units as half-life

  • h is the half-life

• Growth

  • A(t) = A_o(1+r)^t

  • A is the amount at a given time

  • A_o is the original amount

  • r is the percent rate as a decimal (ex. 1.8% is 0.018)

  • t is the amount of time that has passed

• Compound Interest

  • A = P(1+r/n)^nt

  • A is the account balance after t years

  • P is the beginning principle

  • r is the annual interest rate

  • n is the number of times the interest is compounded per year (ex. biweekly = 26, quarterly = 4)

  • t is the time that has passed, in years

• The number e is approximately 2.72, and y = e^x is frequently used as models of exponential growth

  • e - 1 + 1/1 + 1/(1×2)…

Lesson 2 - Logarithms

• Logarithm - y = log_ax, where a > 0, and a ≠ 1; the inverse of the exponential function y = a^x; the exponents placed on the base to get the arguments

  • The graph of y = log_ax will pass through (1,0)

  • A logarithm with no base is assumed to have base 10

• When solving, change any exponent fractions to a root (ex. x^2/3 = ³√(x²))

Lesson 4 - Laws of Logarithms

• Logarithm rules and properties: