Linear Growth
Author: Andreas Bauer

Experiment with the sliders to vary the charge per minute and the base fee. Consider especially the changes in the explicit and recursive equations and how the two representations depend on each other.

Linear growth

Growth per step:

Starting value:

Explicit equation:

Recursive equation:

n

f(n)

a = 0.5 (slider from 0 to 5, step 0.1)
b = 5 (slider from 0 to 20, step 0.1)
Liste1 = Sequence((n, a * n + b), n, 0.0, 15.0)
A2 = 0
A3 = 1
A4: 2.0 * A3 - A2
A5: 2.0 * A4 - A3
A6: 2.0 * A5 - A4
A7: 2.0 * A6 - A5
A8: 2.0 * A7 - A6
A9: 2.0 * A8 - A7
A10: 2.0 * A9 - A8
A11: 2.0 * A10 - A9
A12: 2.0 * A11 - A10
A13: 2.0 * A12 - A11
A14: 2.0 * A13 - A12
A15: 2.0 * A14 - A13
A16: 2.0 * A15 - A14
A17: 2.0 * A16 - A15
A18: 2.0 * A17 - A16
A19: 2.0 * A18 - A17
A20: 2.0 * A19 - A18
A21: 2.0 * A20 - A19
A22: 2.0 * A21 - A20
A23: 2.0 * A22 - A21
A24: 2.0 * A23 - A22
B2: a * A2 + b
B3: a * A3 + b
B4: a * A4 + b
B5: a * A5 + b
B6: a * A6 + b
B7: a * A7 + b
B8: a * A8 + b
B9: a * A9 + b
B10: a * A10 + b
B11: a * A11 + b
B12: a * A12 + b
B13: a * A13 + b
B14: a * A14 + b
B15: a * A15 + b
B16: a * A16 + b
B17: a * A17 + b
B18: a * A18 + b
B19: a * A19 + b
B20: a * A20 + b
B21: a * A21 + b
B22: a * A22 + b
B23: a * A23 + b
B24: a * A24 + b
Text3: "f(n) = " + a + "\cdot n + " + b
Text6: "f(n+1) = f(n) + " + a + ", with f(0) = " + b