Domain: Range: x-intercept: y-intercept: Increasing: Decreasing: Minimum or Maximum: End Behavior:

EXPONENTIAL GROWTH AND DECAY

NOTES

Example 1 Do you think this problem represents growth or decay?

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

LET’S LOOK AT THE GRAPH…

8000 6696 5604.55

4691.01

3926.38

3286.38

2750.7

2302.33

1927.05

1612.94

1350.03

1129.98

945.792

791.628

662.592

554.59

WHAT CAN YOU SAY ABOUT THE GRAPH?

• Domain: • 𝑡 ≥ 0 • • Increasing: never • Range: • 𝑅 > 0 • Asymptote: • 𝑅 = 0 • • Decreasing: Always • • y-intercept (0, 8000)

Example 2 Let’s make a table and graph…

Let’s make a table and graph… 0 1 2 3 4 5 6 7 8 9 10 11 12 13 8000 11313.7

16000 22627.4

32000 45254.8

64000 90509.7

128000 181019 256000 362039 512000 724077

• • • • • •

WHAT CAN YOU SAY ABOUT THE GRAPH?

Domain:

𝒏 ≥ 𝟎 • •

Increasing: always Range:

𝑨 > 𝟎

Asymptote:

𝑨 = 𝟎 •

Decreasing:

•

never

•

y-intercept

•

(0, 8000)

𝟖𝟎𝟎𝟎 𝒉𝒂 𝟑𝟐, 𝟎𝟎𝟎 𝒉𝒂 ; 𝟗𝟎, 𝟓𝟎𝟎 𝒉𝒂

Which of the following organisms' populations is not likely to exhibit exponential B) gorillas D) rats? growth? A) bacteria C) cockroaches

Gorillas are the largest of the living primates. They are ground-dwelling and predominantly herbivorous. Gestation is 8½ months. There are typically 3 to 4 years between births. Therefore they would not experience exponential growth such as bacteria, cockroaches or rats

YOUR TURN  For each problem include the following: Domain ; Range; Asymptote; y-intercept ; Increasing / Decreasing