linear and Exponential Growth & Decay

0.0(0)
studied byStudied by 0 people
0.0(0)
full-widthCall Kai
learnLearn
examPractice Test
spaced repetitionSpaced Repetition
heart puzzleMatch
flashcardsFlashcards
GameKnowt Play
Card Sorting

1/12

encourage image

There's no tags or description

Looks like no tags are added yet.

Study Analytics
Name
Mastery
Learn
Test
Matching
Spaced

No study sessions yet.

13 Terms

1
New cards

Linear Growth

Occurs when a quantity grows by the same absolute amount in each unit of time

2
New cards

Exponential growth

Occurs when a quantity grows by the same relative (or percentage) amount in each unit of time.

3
New cards

Linear Growth & Decay

Occurs when a quantity grows by the same absolute amount in each unit of time.

  • Constant: The amount of change.

  • Example: A savings account that earns 50 dollars in interest each month.

  • Formula: Can be represented as y = mx + b, where m is the constant absolute change.

4
New cards

Linear growth & Decay

F(x)=mx+b

5
New cards

Doubling

Exponential growth

6
New cards

Linear Growth

Occurs when a quantity grows by the same absolute amount in each unit of time

7
New cards

Exponential growth

Occurs when a quantity grows by the same relative (or percentage) amount in each unit of time.

8
New cards

Linear Growth & Decay

Occurs when a quantity grows by the same absolute amount in each unit of time.

  • Constant: The amount of change.

  • Example: A savings account that earns 50 dollars in interest each month.

  • Formula: Can be represented as y = mx + b, where m is the constant absolute change.

9
New cards

Linear growth & Decay

F(x)=mx+b

10
New cards

Doubling

Exponential growth

11
New cards

Linear Decay

Occurs when a quantity decreases by the same absolute amount in each unit of time.

  • Constant: The amount of change is a negative value (-m).

  • Example: A car depreciating by 500 dollars each year.

  • Formula: Can also be represented as y = mx + b, where m is the constant absolute change (negative for decay).

12
New cards

Exponential Decay

Occurs when a quantity decreases by the same relative (or percentage) amount in each unit of time.

  • Example: The amount of a radioactive substance decreasing by half every X years (half-life).

  • Formula: Can be represented as A(t) = P(1 - r)^t, where P is the initial amount, r is the decay rate (as a decimal), and t is time.

13
New cards

General Formula for Exponential Growth/Decay

A(t) = P(1 \pm r)^t

  • A(t) is the amount after time t.

  • P is the initial amount (principal).

  • r is the growth/decay rate (as a decimal).

  • t is the time.

  • Use (1 + r) for growth and (1 - r) for decay.