VG2
funksjoner
Quiz
What is an exponential function?
Exponential functions describe growth or decay that occurs at a fixed percentage rate — from bank interest to population growth and radioactive decay.
The formula
f(x) = a · bˣ
- a = initial value (when x = 0)
- b = growth factor (b > 0, b ≠ 1)
- b > 1 → growth · 0 < b < 1 → decay
Example — compound interest
10,000 NOK at 4% annual interest for 10 years:
f(10) = 10 000 · 1.04¹⁰ ≈ 14,802 NOK
f(10) = 10 000 · 1.04¹⁰ ≈ 14,802 NOK
Example — half-life
100 g with 5-year half-life, after 20 years:
f(20) = 100 · (0.5)⁴ = 6.25 g
f(20) = 100 · (0.5)⁴ = 6.25 g
The natural number e
e ≈ 2.71828...
f(x) = eˣ is special: it is its own derivative!
Compound interest is the eighth wonder of the world. He who understands it, earns it — he who does not, pays it.
— Albert Einstein (1879–1955)
🧠 Test yourself
Question 1 of 3
What is the growth factor for 12% growth per year?