vmbo kader and gt havo vwo
Exponential growth calculator
Quick answer
N = B · gᵗ, with starting value B, growth factor g and t periods. Growth factor for p% growth: g = 1 + p ÷ 100.
500 growing 4% a year, after 3 years: N = 500 · 1,04^3 = 562,43.
Calculator
Choose what you want to know: the amount after a number of periods, the growth factor over a longer period, or the doubling time or half-life. Answers use a decimal comma (1,04 rather than 1.04), the way Dutch schools write numbers.
What is exponential growth?
With exponential growth an amount is multiplied by the same number every period. That number is the growth factor g (Dutch: groeifactor). With linear growth the same amount is added each period; with exponential growth the part that gets added keeps growing too.
If g is greater than 1, the amount increases. If g lies between 0 and 1, it decreases. From percentage to growth factor: p% growth gives g = 1 + p ÷ 100, and p% decrease gives g = 1 − p ÷ 100. So 4% growth goes with g = 1,04 and a 20% decrease with g = 0,8.
The formula is N = B · gᵗ. B is the starting value (the amount at t = 0, Dutch beginwaarde) and t is the number of periods. Make sure t and g refer to the same period: a growth factor per year goes with t in years.
The doubling time is how long it takes for the amount to become twice as large; the half-life is how long it takes to halve. Neither depends on the starting value, only on the growth factor.
Examples by level
A phone costs €300 and loses 20% of its value every year. What is it worth after 3 years?
- Growth factor20% decrease: g = 1 − 20 ÷ 100 = 0,8
- FormulaN = B · gᵗ
- CalculateN = 300 · 0,8^3 = 153,6
After 3 years the phone is worth €153,60.
A bacteria colony grows 12% per hour. What is the doubling time?
- Growth factorg = 1,12 per hour
- Equation1,12ᵀ = 2
- SolveT = log(2) ÷ log(1,12) = 6,12
The doubling time is about 6,12 hours. Without log you can also try values: work out 1,12ᵀ for a few values of T until you reach 2.
An amount grows with growth factor 1,05 per year. What is the growth factor per 10 years, and which growth percentage goes with it?
- RuleOver k periods the growth factor is g^k.
- Substitute1,05^10 = 1,6289
- As a percentage(1,6289 − 1) · 100 = 62,89% increase
Over 10 years the amount grows by about 62,89%, not by 10 · 5% = 50%.
Common mistakes
Wrong
With a 20% decrease per year, subtracting 20% of the starting value every year.
Right
Multiply by 0,8 every year. From €300, after 3 years 300 · 0,8^3 = 153,6 is left.
Wrong
For 4% growth, using 4 or 0,04 as the growth factor.
Right
The growth factor is 1 + 4 ÷ 100 = 1,04.
Wrong
Working out B · g · t instead of B · gᵗ.
Right
t is an exponent: you multiply by g t times.
Wrong
For 10 years, multiplying the yearly percentage by 10.
Right
The growth factor per 10 years is g^10, as in the vwo example above.
To practice with an explanation for every mistake, try exponential growth practice.
Exponential growth on the Dutch exam
The 2027 central exam syllabus for wiskunde A havo (subdomain C5) asks you to calculate with starting value, growth factor, growth percentage, half-life and doubling time. For wiskunde B havo and vwo it asks you to find the doubling time and half-life of exponential growth processes. In wiskunde A vwo, starting value, growth factor, growth percentage, half-life and doubling time are part of the knowledge you are expected to have ready.
In vmbo, the kader track uses the terms growth factor and starting value. The gemengd/theoretisch track adds a formula of the form y = b · gᵗ, doubling time and half-life, and compound interest.
Next step
- How does this work? The explanation and examples are further up this page.
- Test yourself Exponential growth practice, with an explanation after every answer.
Learning path
- Learn first: Percentage calculator Percent of a number, part-whole, and percent change.
Frequently asked questions
How do you turn a growth percentage into a growth factor?
For growth, add the percentage divided by 100 to 1; for decay, subtract it from 1. 4% growth gives growth factor 1,04; a 20% decrease gives growth factor 0,8.
What is the difference between linear and exponential growth?
With linear growth the same number is added every period. With exponential growth the amount is multiplied by the same number every period: the growth factor.
How do you calculate the doubling time?
Solve gᵀ = 2: T = log(2) ÷ log(g). With 12% growth per hour, g = 1,12 and T = log(2) ÷ log(1,12) = 6,12 hours. For the half-life you solve gᵀ = 0,5.