Chapter 3 Notes on Exponential and Logarithmic functions

(The above two examples will help you with MathXL problems #1-4)

(Example #3 matches MathXL problem #4 and 5) ********* ******* ******* ****** ******* ******* ****** ******* ******* ****** ******* ****** ******* ******* ****** ******* ******* ****** ******* ******* ****** ******* ****** ******* ******* ****** ******* ******* ****** ******* ******* ****** ******* ****** ******* ******* **** ********* ******* ******* ****** ******* ******* ****** ******* ******* ****** ******* ****** ******* ******* ****** ******* ******* ****** ******* ******* ****** ******* ****** ******* ******* ****** ******* ******* ****** ******* ******* ****** ******* ****** ******* ******* **** ********* ******* ******* ****** ******* ******* ****** ******* ******* ****** ******* ****** ******* ******* ****** ******* ******* ****** ******* ******* ****** ******* ****** ******* ******* ****** ******* ******* ****** ******* ******* ****** ******* ****** ******* ******* **** ********* ******* ******* ****** ******* ******* ****** ******* ******* ****** ******* ****** ******* ******* ****** ******* ******* ****** ******* ******* ****** ******* ****** ******* ******* ****** ******* ******* ****** ******* ******* ****** ******* ****** ******* ******* **** ********* ******* ******* ****** ******

Graphing Exponential functions: (problems 6 through 9)

Parent function is f(x) = a · bx

If there is no “a” value, it will cross the y-axis at (0,1), regardless of what the base is. If the “b” value is a whole

number with a positive exponent, it will open to the left. As x approaches ∞, y approaches ∞. As x approaches

negative ∞, y approaches zero.

If the “b” value is a fraction, or a whole number with a negative exponent, it will open to the right. (reflect

across the y-axis). As x approaches ∞, y approaches zero. As x approaches negative ∞, y approaches ∞.

If the exponent has something added or subtracted to the x, it will have a horizontal shift. “x - 2” means shift

two units right, and “x + 5” means shift 5 units left. If the exponent has a coefficient, like “3x,” it has a

horizontal shrink.

Exponential Growth and Decay: (problems # 10 through 17)

If the “b” value is greater than 1 (with a positive exponent), the function represents exponential growth. If the

“b” value is less than one (or has a negative exponent), the function represents exponential decay.

The end behavior is the same as the info in the section above on graphing.

To find the constant percentage rate of growth or decay, use b = 1 + r.

Plug in the b-value, and solve for r. If r is positive (meaning your b-value is greater than 1, the function

represents exponential growth. If r is negative (meaning your b-value is less than 1), it represents exponential

decay. Convert the r-value to a percent to get the constant percentage rate. (If r is negative, make it positive for

the percentage).

SKIP PROBLEMS # 18, 19, 20, AND 21. (I will adjust MathXL scores as needed)

Logarithms: (problems # 22 through 34)