6.2 Exponential FunctionsNotes

•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 = ax2+bx+c

• Exponential looks

like: y = a•bx

y = a•bx

coefficient base

exponent

Examples:

•f(x) = (77 – x)x•g(x) = 0.5x – 3.5•h(x) = 0.5x2 + 7.5

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

( ) 1nt

rA t P

n

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)

1*10.05

( ) 100 11

A t

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)

4*10.05

( ) 100 14

A t

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)

3 *1065

36.05

( ) 1005

1A t