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Exponential growth practice

Practice growth factors, N = B · gᵗ, and doubling time and half-life. When you get one wrong, you see whether, for example, you calculated linearly instead of exponentially.

Practice session

What you practise

Level 1: the growth factor from a percentage. Level 2: the amount after a few periods. Level 3: longer periods and the growth percentage over several years. Level 4: doubling time and half-life, mixed with the rest. The explanation and a calculator are on the exponential growth calculator page. Numbers use a decimal comma (1,04), as in Dutch schools.

Example

Find the amount after 3 periods when the starting value is 500 and the amount grows by 4% each period.

  1. Growth factor: g = 1 + 4 ÷ 100 = 1,04
  2. N = B · gᵗ
  3. N = 500 · 1,04^3 = 562,43

Answer: 562,43.

What you need to know

What the 2027 exam syllabus says about growth processes, as far as this module practices it.

havo · wiskunde A · subdomain C5

Calculating with starting value, growth factor, growth percentage, half-life or doubling time · source syllabus wiskunde A havo 2027 (Examenblad)

havo and vwo · wiskunde B

Finding the doubling time and half-life of exponential growth processes · sources syllabus wiskunde B havo 2027 (Examenblad), syllabus wiskunde B vwo 2027 (Examenblad)

vmbo · kader and gemengd/theoretisch · WI/K/4

Kader: the terms growth factor and starting value. Gemengd/theoretisch also: y = b · gᵗ, doubling time and half-life, and compound interest · source syllabus wiskunde vmbo 2027 (Examenblad)

Formula sheet

Print-friendly: use Print in your browser.

  • Exponential growth N=B·gt
  • Growth factor for p% growth g=1+p100
  • Growth factor over k periods gk
  • Doubling time T=log(2)log(g)
Growth factor (groeifactor)

The number the amount is multiplied by every period.

Half-life (halveringstijd)

The time it takes for a decreasing amount to halve.

Practice with real exam questions on Examenblad.nl (in Dutch). We do not host past exams.

Frequently asked questions

How precise does my answer need to be?

A growth factor has to be exact, for example 1,04. Round amounts, percentages and times to 2 decimal places; anything within 0,02 counts as correct.

Can I work out the doubling time without log?

Yes. Try values of T until gᵀ is about 2. Do round to 2 decimal places, as the question says.