Model, graph, and compare arithmetic, geometric, and exponential relationships.
Common CoreF-BF.A.2F-LE.A.1F-LE.A.2F-IF.A.3
7 lessons25 short videos6 key concepts, out loud
10.1
Arithmetic Sequences
Add the same amount each step
F-BF.A.2F-LE.A.2
Key idea
An arithmetic sequence changes by adding or subtracting a constant value called the common difference, which can be represented recursively, explicitly as a linear function, or graphed as discrete points.
Learn how to identify the common difference of an arithmetic sequence, write recursive and explicit formulas, and connect these patterns to linear functions.
Key concept · Lesson 10.1
Nineteen jumps reach the twentieth term
Listen0:00 / 0:22
Transcript. Every step of an arithmetic sequence adds d, the common difference. In the formula, a sub n is the term you want, a sub one is the starting term, and n is the step number. Add d to the starting term n minus one times, because step twenty takes nineteen jumps.
10.2
Geometric Sequences
Multiply by the same factor each step
F-BF.A.2F-IF.A.3
Key idea
A geometric sequence is a pattern of numbers where each term is found by multiplying the previous term by a constant common ratio, which can be modeled using explicit and recursive formulas.
Learn how to identify the common ratio of a geometric sequence and write explicit and recursive formulas to find any term in the pattern.
Key concept · Lesson 10.2
Count the multiplies, not the steps
Listen0:00 / 0:22
Transcript. A geometric sequence multiplies by the same common ratio every step, so you never add. To reach step n you multiply the first term by r one time less than n. That is why the exponent is n minus one. Here step six uses three to the fifth.
10.3
Exponential Growth & Decay Models
Build and read y = a times b to the x
F-LE.A.2
Key idea
In the exponential model y = a(b)^x, 'a' represents the initial value and 'b' represents the growth factor (if b > 1) or decay factor (if 0 < b < 1) per unit of change.
Learn how to build and interpret exponential equations of the form y = a(b)^x to model real-world growth and decay.
Key concept · Lesson 10.3
Read a as the start, b as the factor
Listen0:00 / 0:24
Transcript. Read the model in two pieces. The letter a is the starting value, what you have when x is zero. The letter b is the multiplier for each step. Above one it grows, between zero and one it shrinks. A six percent rise makes b one point zero six, not zero point zero six.
10.4
Graphing Exponential Curves
Curves that climb or fade; the asymptote
F-IF.C.7e
Key idea
Graph exponential functions of the form y = a * b^x to show rapid growth or decay, and identify the horizontal asymptote as the boundary line the curve approaches but never crosses.
Learn how to graph exponential growth and decay curves by plotting key points and identifying the horizontal asymptote.
Key concept · Lesson 10.4
Three points, then hug the asymptote
Listen0:00 / 0:23
Transcript. Use three easy inputs: negative one, zero and one. Here they give one half, one and two, enough to shape the curve. The dashed line is the asymptote. The curve gets closer and closer but never touches it, and you write it as a y value, never an x value.
10.5
Percent Growth in Action (N = P(1+r)^t)
Growth that builds on itself
F-LE.A.2
Key idea
To model exponential growth, use N=P(1+r)^t, where the initial population P grows by a constant percentage rate r over t time periods.
Learn how to write and evaluate exponential equations that model a population growing by a constant percentage over time.
Key concept · Lesson 10.5
Add the rate to 1, then raise it
Listen0:00 / 0:20
Transcript. Percent growth builds on itself, so the new total earns the next increase. Turn the percent into a decimal, add it to one, and that becomes the base. Four percent gives one point zero four. Raise it to the number of periods, then multiply by the starting amount.
10.6
Linear vs. Exponential Growth
Adding the same amount vs. multiplying by the same factor
F-LE.A.1
Key idea
Linear growth increases or decreases by a constant difference over equal intervals, whereas exponential growth changes by a constant ratio, meaning that any positive exponential growth will eventually surpass any linear growth.
Learn how to distinguish between linear and exponential relationships in tables, graphs, and stories, and see why multiplying eventually beats adding.
Key concept · Lesson 10.6
Adding versus multiplying
Listen0:00 / 0:23
Transcript. A linear pattern adds the same amount every step, so its differences stay equal. An exponential pattern multiplies by the same factor, so its ratios stay equal. Adding looks bigger at first, but multiplying always catches up and then races away. Check whether you add or multiply.
10.7
Review & Assessment
Sequences and exponential modeling
Review, practice, quiz and test
Key idea
Review sequences and exponential modeling with targeted practice, a practice test, and a chapter test.
This is one chapter of the climb.
Algebra 1 spans 16 chapters, every lesson taught on video with a key concept you can hear, and Vector on hand to answer questions out loud.
