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- Applications of Exponential and Logarithmic Functions

Still Confused?

Try reviewing these fundamentals first.

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Try reviewing these fundamentals first.

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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

8.

Applications of Exponential and Logarithmic Functions

8.1

Exponential growth and decay by a factor

8.2

Exponential decay: Half-life

8.3

Exponential growth and decay by percentage

8.4

Finance: Compound interest

8.5

Continuous growth and decay

8.6

Logarithmic scale: Richter scale (earthquake)

8.7

Logarithmic scale: pH scale

8.8

Logarithmic scale: dB scale

8.9

Finance: Future value and present value

We have over 770 practice questions in NZ Year 13 Maths for you to master.

Get Started Now8.1

Exponential growth and decay by a factor

8.2

Exponential decay: Half-life

8.3

Exponential growth and decay by percentage

8.4

Finance: Compound interest

8.5

Continuous growth and decay

8.6

Logarithmic scale: Richter scale (earthquake)

8.7

Logarithmic scale: pH scale

8.8

Logarithmic scale: dB scale

8.9

Finance: Future value and present value