Identifying Exponential Growth vs. Decay from Context
Grade 9 students in California Reveal Math Algebra 1 learn to classify real-world exponential situations as growth or decay using context clues and the base b. Words like increases, grows, appreciates, or earns signal growth with formula y=a(1+r)^t and base b=1+r>1. Words like decreases, decays, depreciates, or loses signal decay with formula y=a(1-r)^t and base b=1-r between 0 and 1. For example, a car losing 15% of its value per year uses b=0.85 (decay), while a town growing 3% annually uses b=1.03 (growth). Always verify the base confirms the context.
Key Concepts
A situation represents exponential growth when the quantity increases over time and exponential decay when the quantity decreases over time.
Use the clues below to identify the type and select the correct formula:.
Common Questions
What context clues signal exponential growth?
Words like increases, grows, appreciates, earns, or gains signal growth. The formula is y=a(1+r)^t and the base b=1+r is greater than 1.
What context clues signal exponential decay?
Words like decreases, decays, depreciates, loses, or falls signal decay. The formula is y=a(1-r)^t and the base b=1-r is between 0 and 1.
How do you write an exponential equation for a car losing 15% value per year?
The word loses signals decay. Use y=a(1-r)^t with r=0.15: y=a(0.85)^t. Since 0.85<1, the base confirms this is decay.
How do you write an exponential equation for a town growing 3% annually?
The word grows signals growth. Use y=a(1+r)^t with r=0.03: y=a(1.03)^t. Since 1.03>1, the base confirms this is growth.
How do you identify growth or decay from a table of values?
Compute the ratio between consecutive outputs. If the ratio b>1, it is growth. If 0<b<1, it is decay. For outputs 100, 50, 25, 12.5, the ratio is 1/2=0.5, confirming decay.
Which unit covers identifying exponential growth and decay?
This skill is from Unit 8: Exponential Functions in California Reveal Math Algebra 1, Grade 9.