1. E-4. 4: Constant Ratios in the context of Real-world Situations E-4
E-4.4: Constant Ratios in the context of Real-world Situations E-4.6: Homework E-5.2: Deepening Our Understanding of Exponential Functions

2. Answers for Page: 139

3. Answers for Page:
2.A. f(x) = -4x+13 2.B. f(x) = 2x-6 3. f(x) = 3x-5 4. f(x) = 3x-7 5. See right 6. Linear + or – and Exponential * or ÷ Linear is a line and Exponential is a curve

4. Essential Question: How is exponential functions used in the real world?
Key words for exponential growth: double, triple, grows, add Key words for exponential decay: depreciate, loses value, halves

5. General Form of an Exponential Function
GROWTH: DECAY:

6. Reminder about Constant Ratio
What is the constant ratio?
2. How do I find future values?
3. How do I find previous values?
4. What is the initial value?
5. What is the equation? x
F(x) 3
192 4
768

7. Reminder about Constant Ratio
1. What is the constant ratio? =4
2. How do I find future values? Multiply the prev. output by 4
3. How do I find previous values? Divide the prev. output by 4
4. What is the initial value? 3
5. What is the equation?
𝑓 𝑥 =3∗ 4 𝑥 x
F(x) 3 1 12 2 48
192 4
768 5
3072

8. Reminder about Constant Ratio
What is the constant ratio?
2. How do I find future values?
3. How do I find previous values?
4. What is the initial value?
5. What is the equation? x
F(x) -3 32 -2 16

9. Reminder about Constant Ratio
What is the constant ratio? =0.5
2. How do I find future values? Multiply the prev. output by 0.5
3. How do I find previous values? Divide the prev. output by 0.5 (AKA multiply by 2)
4. What is the initial value? 4
5. What is the equation?
𝑓 𝑥 =4∗ 0.5 𝑥 x
F(x) -3 32 -2 16 -1 8 4 1 2