Math 1 Strand
Build confidence with growth, decay, sequences, and exponential models in context.
Exponential relationships help students recognize patterns that do not grow by a constant amount. In Math 1, the big move is seeing when outputs multiply by a constant factor and explaining what that factor means in the situation.
In y = abx, a is the initial value and b is the growth or decay factor. If b > 1, the pattern grows. If 0 < b < 1, the pattern decays.
Standards-Aligned Overview
Based on the Math 1 Standards for exponential functions, geometric sequences, and model comparison.
Choose linear or exponential models and justify the choice from equal differences or equal factors.
Compare long-term behavior and explain why exponential growth eventually passes linear growth.
Interpret the parameters a and b in y=ab^x in context.
Interpret and explain growth and decay rates for exponential functions.
Build linear and exponential functions from descriptions, graphs, tables, and ordered pairs.
Translate between explicit and recursive forms of geometric sequences.
Key Vocabulary
These terms support tables, graphs, equations, and context questions.
A function that changes by multiplying by the same factor over equal input intervals.
The starting output, often the value when x=0. In y=ab^x, it is a.
The number multiplied each step when an exponential function increases. In y=ab^x, it is b when b>1.
The percent increase compared with the previous amount. A 20% growth rate uses a factor of 1.20.
The number multiplied each step when an exponential function decreases. In y=ab^x, it is b when 0<b<1.
The percent decrease from the previous amount. A 30% decay rate means the factor kept is 0.70.
The repeated factor between consecutive output values in an exponential table.
How much the output changes per 1-unit input change. Exponential functions do not have a constant rate of change.
A pattern with equal differences between output values over equal input intervals.
A sequence where each term is found by multiplying the previous term by the same factor.
A rule that gives the first term and explains how to use one term to find the next term.
A rule that lets you find any term or output directly from the input.
Student-Friendly Review
Keep the reasoning simple: starting value, repeated factor, then what the model means.
For f(x) = 3(2)x, the initial value is 3 and the growth factor is 2.
A 15% decrease keeps 85%, so use 0.85x. A 20% increase uses 1.20x.
Equal differences mean linear. Equal ratios, like multiplying by 1/2, mean exponential.
Linear patterns add the same amount. Exponential patterns multiply by the same factor.
Practice Questions
Start with DOK 1 fluency, then build toward applications, analysis, and EOC-style mixed practice.
Practice Set 1
Growth, decay, initial value, and constant factors
Practice Set 2
Tables, contexts, and model selection
Practice Set 3
Compare models and justify choices
Practice Set 4
Linear vs. exponential decisions across representations
Practice Set 5
More connected growth, decay, and context practice
Practice Set 6
A compact EOC-style readiness check