The worksheets themselves are in German – just as in class. The editor is only available in German so far.
Exponential functions – worksheets to print
Exponential functions f(x) = a · bˣ: tables of values, a and b from a graph or from two points, growth and decay in percent, linear or exponential, and simple exponential equations.
- Choose the number of tasks and the difficulty yourself
- With an answer sheet and, if you like, a QR code to the answers
- At three levels (★ to ★★★) and as group A and B
- As a single worksheet or as a task on a mixed worksheet
Exponential functions: explained simply
In an exponential function f(x) = a · bˣ, each step of 1 to the right multiplies the value by the same factor b. a is the starting value at x = 0.
How to work it out
- a = f(0) is the starting value, b the growth factor.
- b > 1: growth of (b − 1) · 100 %, for example b = 1.05 → plus 5 %.
- 0 < b < 1: decay of (1 − b) · 100 %, for example b = 0.8 → minus 20 %.
- Linear: equal differences. Exponential: equal ratios.
An example, step by step
Complete the table of f(x) = 3 · 2ˣ for x = 0, 1, 2, 3.
- f(0) = 3 · 2⁰ = 3 · 1 = 3.
- Each step doubles: f(1) = 6, f(2) = 12.
- f(3) = 24.
Understand other variations
Negative x
f(−1) = 3 · 2⁻¹ = 3 · 0.5 = 1.5. A step to the left divides by b.
From two points
P(0|3) and Q(2|12): a = 3, b² = 12 : 3 = 4, so b = 2.
Growth and decay
Savings grow by 5 % a year: b = 1.05. The value of a car falls by 15 % a year: b = 0.85.
Exponential equations
3 · 2ˣ = 96: divide by 3, then 2ˣ = 32. Since 2⁵ = 32, x = 5.
Your turn
f(x) = 100 · 0.5ˣ. Work out f(3).
Show the answer and method
100 · 0.5 · 0.5 · 0.5 = 12.5.
Ready-made worksheets: Exponential functions
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