Lesson Notes By Weeks and Term v4 - SHS 2
PATTERNS AND RELATIONS
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PATTERNS AND RELATIONS
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Subject: Mathematics
Class: SHS 2
Term: 1st Term
Week: 19
Grade code: 2.2.2.LI.5
Strand code: 2
Sub-strand code: 2
Content standard code: 2.2.2.CS.1
Indicator code: 2.2.2.LI.5
Theme: ALGEBRAIC REASONING
Subtheme: PATTERNS AND RELATIONS
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This lesson introduces the concept of exponential growth, a powerful mathematical idea that describes how things can increase at an accelerating rate. We see this pattern everywhere in Ghana and around the world – from the way our population grows, to how money earns interest in a bank, or even how information spreads on social media. Understanding this concept helps us make better predictions and informed decisions about our future, our finances, and our communities. We will connect this to the idea of Geometric Progressions, which you have studied earlier, and develop a straightforward formula to model and solve real-world problems.
What is Exponential Growth?
Imagine you have two job offers for a 5-day project. Offer A (Linear Growth): You get GHS 100 on Day 1, and your pay increases by a fixed GHS 100 each day. Offer B (Exponential Growth): You get GHS 10 on Day 1, and your pay doubles each day.
Let's see the earnings:
| Day | Offer A (Linear) | Offer B (Exponential) | | :-- | :--- | :--- | | 1 | GHS 100 | GHS 10 | | 2 | GHS 200 (100+100) | GHS 20 (10 x 2) | | 3 | GHS 300 (200+100) | GHS 40 (20 x 2) | | 4 | GHS 400 (300+100) | GHS 80 (40 x 2) | | 5 | GHS 500 (400+100) | GHS 160 (80 x 2) |