Math 1 · Unit 7
Introduction to Exponential Functions
Six lessons: a new family that multiplies, the form y = a · bx, growth and decay, reading the graph, linear or exponential, and building and using exponential models. Lines add the same amount every step; exponentials multiply by the same number every step, and multiplying by 1 is doing nothing.
A New Family That Multiplies
A second family of graphs. Lines add the same amount every step; exponentials multiply by the same number every step. Doubling stories, constant difference versus constant ratio, exponents as repeated multiplying, and why anything to the zero power is 1.
Start Unit 7, Lesson 1The Form y = a · bx
The three family questions for the exponential family: the form y = a times b to the x, the parameters a and b, and their jobs. a is the starting value and y-intercept because b to the zero is 1; b is the growth factor you multiply by each step. Build tables, plot, and move the sliders.
Start Unit 7, Lesson 2Growth and Decay
b bigger than 1 grows, b between 0 and 1 decays, and b exactly 1 is a flat line, because multiplying by more than 1 makes things bigger and by less than 1 makes them smaller. Then percents: grows 10% is a factor of 1.10, loses 25% is 0.75, both directions.
Start Unit 7, Lesson 3Reading the Graph
The key features of an exponential graph, each traced back to a or b: y-intercept (0, a), domain all reals, range y greater than 0, the horizontal asymptote y = 0 and why the curve never touches it, end behavior said plainly and then in math words, and matching equations to graphs by elimination.
Start Unit 7, Lesson 4Linear or Exponential?
The deciding test. From a table: equal x steps, then subtract for a constant difference (linear) or divide for a constant ratio (exponential). From a story: fixed amounts add, doubles and percents multiply. Town A adds 10 a year, Town B grows 10% a year, and the exponential eventually passes any line.
Start Unit 7, Lesson 5Building and Using Exponential Models
Build an exponential model from a story, table, or two points, then use it. Forward: evaluate, power first. Backward: a table, or a horizontal target line and the crossing point. Say what a and b mean, decide discrete or continuous, and ask what changes if a or b changes.
Start Unit 7, Lesson 6Printables for Unit 7
Study guides, worksheets with answer keys, and lesson plans for every lesson in this unit.