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Get Started Now- Lesson: 19:41

The growth/decay factor "(1+r)" dictates the rate of exponential growth and decay. We will work on questions related to growth/decay factor in this lesson.

Related concepts: Derivative of inverse trigonometric functions, Derivative of logarithmic functions,

exponential growth/decay: ${ A_f = A_i (f)^{time\over period}}$

${A_f}$: final amount

${A_i}$: initial amount

${f }$ : growth/decay factor

half-time$\to f = {1\over 2}$

triple$\to f = {3}$

ten-fold$\to f = {10}$

increase by 10%$\to f = {({1 + {10\over 100}}) } { = 1.1}$

decrease by 8%$\to f = {({1 - {8\over 100}}) } { = 0.92}$

${time}$ : total time given

${period}$ : every length of time

${A_f}$: final amount

${A_i}$: initial amount

${f }$ : growth/decay factor

half-time$\to f = {1\over 2}$

triple$\to f = {3}$

ten-fold$\to f = {10}$

increase by 10%$\to f = {({1 + {10\over 100}}) } { = 1.1}$

decrease by 8%$\to f = {({1 - {8\over 100}}) } { = 0.92}$

${time}$ : total time given

${period}$ : every length of time

- 1.triple growth

A certain type of bug can triple its population every 10 years.

How many bugs will there be in 50 weeks if there are 76 bugs today?

24.

Functions: Linear, Quadratic, Exponential

24.1

Graphing exponential functions

24.2

Graphing transformations of exponential functions

24.3

Finding an exponential function given its graph

24.4

Exponential growth and decay by a factor

24.5

Exponential decay: Half-life

24.6

Exponential growth and decay by percentage

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