Question

40% growth, 20% decay, 60% growth, 80% growth, 20% growth, 40% decay, 80% decay, 60% decay; and equations: 20(0.6)^t = 1.2, 40(0.2)^t = 1.6, 60(0.8)^t = 1.4, 1.2(1.4)^t = 80, 80(1.6)^t = 20, each with an arrow to a blank box

Explanation:

Step1: Identify decay/growth factor

For exponential equations of the form $A(b)^t = C$:

• If $b > 1$, it is growth: growth rate = $b - 1$
• If $0 < b < 1$, it is decay: decay rate = $1 - b$

Step2: Analyze $20(0.6)^t=1.2$

$b=0.6$, decay rate = $1 - 0.6 = 0.4 = 40\%$

Step3: Analyze $40(0.2)^t=1.6$

$b=0.2$, decay rate = $1 - 0.2 = 0.8 = 80\%$

Step4: Analyze $60(0.8)^t=1.4$

$b=0.8$, decay rate = $1 - 0.8 = 0.2 = 20\%$

Step5: Analyze $1.2(1.4)^t=80$

$b=1.4$, growth rate = $1.4 - 1 = 0.4 = 40\%$

Step6: Analyze $80(1.6)^t=20$

$b=1.6$, growth rate = $1.6 - 1 = 0.6 = 60\%$ (Note: The equation shows a decrease over time despite the growth factor, but the factor itself defines the growth rate classification)

Answer:

1. $20(0.6)^t = 1.2$ → 40% decay
2. $40(0.2)^t = 1.6$ → 80% decay
3. $60(0.8)^t = 1.4$ → 20% decay
4. $1.2(1.4)^t = 80$ → 40% growth
5. $80(1.6)^t = 20$ → 60% growth