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- Applications of Exponential Functions

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Get Started Now- Lesson: 18:51
- Lesson: 27:32

Exponential growth/decay rates can be presented in percentages. We will work on questions of this kind in this lesson.

Basic concepts: Solving logarithmic equations,

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.exponential growth/decay by percentage

The population of rabbits is increasing by 70% every 6 months.

Presently there are 500 rabits. How many years will it take for

the population to reach 1,000,000? - 2.exponential growth/decay by percentage

The intensity of light is reduced by 2% for each meter that a diver

descends below the surface of the water. At what depth is the intensity of

light only 10% of that at the surface?

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