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- Precalculus
- Exponential and Logarithmic functions

Still Confused?

Try reviewing these fundamentals first

Still Confused?

Try reviewing these fundamentals first

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Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started Now- Lesson: 1a4:34
- Lesson: 1b3:06
- Lesson: 1c3:50
- Lesson: 1d3:23
- Lesson: 1e3:21
- Lesson: 26:41

Now that we understand the concepts behind exponential growth and decay, let's utilize them and solve real-life problems! One of the many areas where exponential growth comes in handy is Finance. In this section, we will learn how compound interest helps us grow our deposits in our investment and/or bank accounts.

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

exponential growth/decay: ${ A_f = A_i (1+\frac{r}{n})^{nt}}$

${A_f}$: final amount

${A_i}$: initial amount

${r}$ : Annual interest rate

${t}$: total time given in**years **

${n}$ : number of times compounded in a year, if

${A_f}$: final amount

${A_i}$: initial amount

${r}$ : Annual interest rate

${t}$: total time given in

${n}$ : number of times compounded in a year, if

Compound daily: |
n = 365 |

Compound monthly: |
n = 12 |

Compound quarterly: |
n = 4 |

Compound semi-annually: |
n = 2 |

Compound annually: |
n = 1 |

- 1.Bianca deposits $1,000 in a savings account with an annual interest rate of

12%. How much money will she have in 20 years, if the interest is compounded:a)dailyb)monthlyc)quarterlyd)semi-annuallye)annually - 2.A $1000 investment, compounded quarterly, doubles in value over a period

of 8 years. Find the interest rate per annum.

6.

Exponential and Logarithmic functions

6.1

Converting from logarithmic form to exponential form

6.2

Evaluating logarithms without calculator

6.3

Common logarithms

6.4

Evaluating logarithms using change-of-base formula

6.5

Converting from exponential form to logarithmic form

6.6

Product rule of logarithms

6.7

Quotient rule of logarithms

6.8

Combining product rule and quotient rule in logarithms

6.9

Solving logarithmic equations

6.10

Evaluating logarithms using logarithm rules

6.11

Continuous growth and decay

6.12

Finance: Compound interest

6.13

Exponents: Product rule $(a^x)(a^y)=a^{(x+y)}$

6.14

Exponents: Division rule ${a^x \over a^y}=a^{(x-y)}$

6.15

Exponents: Power rule $(a^x)^y = a^{(x\cdot y)}$

6.16

Exponents: Negative exponents

6.17

Exponents: Zero exponent: $a^0 = 1$

6.18

Exponents: Rational exponents

6.19

Graphing exponential functions

6.20

Graphing transformations of exponential functions

6.21

Finding an exponential function given its graph

6.22

Logarithmic scale: Richter scale (earthquake)

6.23

Logarithmic scale: pH scale

6.24

Logarithmic scale: dB scale

6.25

Finance: Future value and present value

6.1

Converting from logarithmic form to exponential form

6.2

Evaluating logarithms without calculator

6.3

Common logarithms

6.4

Evaluating logarithms using change-of-base formula

6.5

Converting from exponential form to logarithmic form

6.6

Product rule of logarithms

6.11

Continuous growth and decay

6.12

Finance: Compound interest

6.13

Exponents: Product rule $(a^x)(a^y)=a^{(x+y)}$

6.14

Exponents: Division rule ${a^x \over a^y}=a^{(x-y)}$

6.15

Exponents: Power rule $(a^x)^y = a^{(x\cdot y)}$

6.16

Exponents: Negative exponents

6.18

Exponents: Rational exponents

6.22

Logarithmic scale: Richter scale (earthquake)

6.23

Logarithmic scale: pH scale

6.24

Logarithmic scale: dB scale

6.25

Finance: Future value and present value