6.2 Exponential Functions Notes Linear, Quadratic, or Exponential? Exponential Growth or Decay? Match Graphs Calculate compound Interest

Linear, Quadratic, or Exponential? Linear looks like: y = mx+b Quadratic looks like: y = ax 2 +bx+c Exponential looks like: y = ab x y = ab x coefficientbase exponent

Examples: f(x) = (77 – x)x g(x) = 0.5 x – 3.5 h(x) = 0.5x

Growth or Decay? Growth if: – base>1 and – exponent is positive Decay if: – base<1 or – exponent is negative Growth if (unusual case): – base<1 and exponent is negative

Examples: f(x) = 500(1.5) x d(x) = 0.125(½) x s(k) = 0.5(0.5) k f(k) = 722 -k

Growth looks like: Base is smaller.Base is larger.

Decay looks like: Base is smaller.Base is larger.

Compound Interest A = amount after t years P = principal (original money) r = interest rate n = number of compounds per year t = time in years

Vocabulary annually = 1 time per year semiannually = 2 times per year quarterly = 4 times per year monthly = 12 times per year daily = 365 times per year

Example Find the final amount of a $100 investment after 10 years at 5% interest compounded annually, quarterly, and daily. P = 100, t = 10, r =.05, n = 1, 4, 365 (3 calcs)

Example, part 2 Find the final amount of a $100 investment after 10 years at 5% interest compounded annually, quarterly, and daily. P = 100, t = 10, r =.05, n = 1, 4, 365 (3 calcs)

Example, part 3 Find the final amount of a $100 investment after 10 years at 5% interest compounded annually, quarterly, and daily. P = 100, t = 10, r =.05, n = 1, 4, 365 (3 calcs)