Unit 6

6-1

100

An exponential function where the multiplier (or b) is < 1

Exponential Decay

200

the starting amount or y-intercept of the graph or equation. In the equation y = a*b^x it is the value of a.

initial value

300

A function where the variable is in the exponent. Graphically it resembles a curve shape.

Exponential Function

400

The line (y = a number) that our function approaches but will never quite touch or cross

Horizontal Asymptote

500

The y-intercept is (0, 2)
The horizontal aysmptote is y = 1
The Domain is all real numbers
The Range is y > 1

Sketch the graph.

6-2

100

What type of pattern do linear functions have?

Adds by the same number every time

200

What type of pattern do exponential functions have?

Multiplies by the same number every time

300

If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

$2,225.54

400

John invested $400 at a rate of 35% for 8 months, compounded continuously. How much is his investment worth after 8 months?

$505.12

500

Heather invested $8,000 in a 4-year Certificate of Deposit (CD) that pays 4.1% interest compounded annually. What is the value of the CD at the end of the 4 years?

$9,394.92

6-3

100

The function f(x) = log_bx is the ___________ function with base _________.

logarithmic, b

200

Logarithmic functions are the inverse of ___.

Exponential Functions

300

Rewrite 34 = 81 in logarithmic form.

log₃81 = 4

400

Rewrite log₆36 = 2 in exponential form.

6²=36

500

log₂(1/8)

-3

Final

500

2log3x² + 3log4x³ = 4log2x² +4log6x

x > 0

x = 36