Exponential functions – Grade 11 math lesson
Lesson 12 of 23 in the Grade 11 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 11 (ages 16–17) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Grade
- Grade 11 (ages 16–17)
- You need
- Paper, a pencil and this page
- Graded
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is graded straight away with a worked explanation, so you never have to grade anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “Why does an exponential function always overtake a linear one in the end?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Confusing linear and exponential tables. Check differences (linear) and ratios (exponential).
- Using the percentage as the factor (5% growth as b = 5). 5% growth means b = 1.05.
Tip for home: Talk about how savings or populations grow over time.
What your child will learn
Learning goal: recognize, write and solve exponential functions and models.
Success looks like
- I can tell linear and exponential relationships apart.
- I can write an exponential model.
- I can solve simple exponential equations.
Key words
- exponential function
- y = a·bˣ
- growth factor
- the number multiplied each step
- decay
- decreasing by a constant factor
- logarithm
- the exponent needed to reach a number
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Fold a sheet of paper in half again and again and record how many layers you get.
The big ideas (for the adult)
An exponential function has the form y = a·bˣ: the starting value a is multiplied by the factor b each time x goes up by 1.
If b > 1 it shows growth; if 0 < b < 1 it shows decay. Linear functions add the same amount; exponential functions multiply by the same amount.
Logarithms undo exponents: if 2ˣ = 32, then x = log₂ 32 = 5.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Graded by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, graded by Classfern |
| Independent practice | 15 min | Graded by Classfern |
| Closure and exit ticket | 6 min | Graded by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are graded by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all graded instantly.
More practice
More Grade 11 math lessons
- Complex numbers
- Radicals
- Vectors
- Laws of exponents
- Square roots and cube roots
- Systems of equations
- Rational expressions and polynomials
- Arithmetic and geometric sequences
- Iteration
- Functions
- Graphing functions
- Trigonometric functions
- Law of sines and law of cosines
- Coordinate geometry
- Counting outcomes
- Experimental probability
- Compound events
- Conditional probability
- Expected value
- Box plots and interquartile range
- Scatter plots and lines of fit
- Sampling and making inferences
Curriculum
Common Core State Standards HSF.BF.B.5: “(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.”
Common Core State Standards HSA.SSE.B.3.c: “Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15^(t) can be rewritten as (1.15^(1/12))^(12t) ≈ 1.012^(12t) to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.