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- Applications of Exponential and Logarithmic Functions

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Get Started Now- Lesson: 18:19
- Lesson: 29:53

In this section, we will bridge the gap between chemistry and mathematics by studying one of the many applications of logarithmic functions. We will learn about the pH Scale and explore how this logarithmic scale can be used to measure the acidity or basicity of a solution.

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

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

- 1.Pure water has a pH of 7. Vinegar has a pH of 3.

Complete the following 2 sentences:

(i) Pure water is __________ times as alkaline as vinegar.

(ii) Vinegar is __________ times as acidic as pure water. - 2.Lemon juice has a pH of 2.5.

Stomach acid is 8 times more acidic than lemon juice.

Tomato juice is 90 times more basic than lemon juice

Find the pH of:

(i)stomach acid

(ii) tomato juice

13.

Applications of Exponential and Logarithmic Functions

13.1

Exponential growth and decay by a factor

13.2

Exponential decay: Half-life

13.3

Exponential growth and decay by percentage

13.4

Finance: Compound interest

13.5

Continuous growth and decay

13.6

Logarithmic scale: Richter scale (earthquake)

13.7

Logarithmic scale: pH scale

13.8

Logarithmic scale: dB scale

13.9

Finance: Future value and present value

We have over 1040 practice questions in AU Year 12 Maths for you to master.

Get Started Now13.1

Exponential growth and decay by a factor

13.2

Exponential decay: Half-life

13.3

Exponential growth and decay by percentage

13.4

Finance: Compound interest

13.5

Continuous growth and decay

13.6

Logarithmic scale: Richter scale (earthquake)

13.7

Logarithmic scale: pH scale

13.8

Logarithmic scale: dB scale

13.9

Finance: Future value and present value