Growing, Growing, Growing

Exponential Growth

100

Carol stocked her pond with 3 fish she expects it to triple every year. After 3 years how many fish are in the pond.

81

200

If you invest $40 in an account for 9 years at a 3% interest rate how much money will you have?

$52

300

If the starting population of 5 rabbits grows at 200% each year, how many will there be 20 years?

5,242,880 rabbits

400

A population of 100 frogs increases at an annual rate of 22%. How many frogs will there be in 5 years?

210

500

A type of bacteria has a very high exponential growth rate at 80% every hour. If there are 10 bacteria, determine how many there will be in 5 hours, in 1 day and in 1 week?

5 hours- 74 Day (24 Hour)-192 1 Week (168 hours)- 1344

Examining Growth Patterns

100

3³

27

200

2⁴

16

300

Bacteria lands on a chair. it multiples by a factor of 4. how much bacteria is on the chair in 3 hours.

64

400

There are 2 spiders living under your bed. They multiply by a factor of 2 each day. how many spiders are there in 3 days.

16

500

4⁴

256

Growth Factors and Growth Rates

100

Suppose there are 100 trout in a lake and the yearly growth factor for the population is 1.5 how many years will it take for the population to double?

between 2 and 3 years

200

find the growth rate associated with the growth factor 1.4

40%

300

Find the growth factor associated with the growth rate 45%

1.45

400

find the growth rate associated with the growth factor 1.75

75%

500

Find the growth factor associated with the growth rate 90%

1.9

Exponential Decay

100

Each year the local country club sponsors a tennis tournament. Play starts with 128 participants. During each round, half of the players are eliminated. How many players remain after 5 rounds?

4

200

Olivia purchased a music system worth $18,000 in the year 2001. It loses its value by 6% per year. What is the value of the music system in 2003?

15840

300

Sarah bought a dish washer for $6,000 in the year 2000. It depreciates by 2% per year. What is the value of the dish washer in 2001?

5880

400

Adam bought a fish aquarium worth $2,000 in the first week of the year. Its value depreciates by 3% per week. What will the value of fish aquarium after 5 weeks?

1700

500

A population of 120,000 goes down by 2% each year. How many people live there in 2 years.

115,200

Patterns with Exponents

100

2^1 X 2^2 = x

x=2^3

200

2^6 = 4^3 = 8^x

x=2

300

3^3 X 3^2 = 3^x

x=5

400

4^3 X x^3 = 4^6

x=4

500

8^4 x 8^7 = x

x =8^11