MYP Maths: Exponential Growth & Decay (Extended) FAQs

Exponential growth and decay describes quantities that change by a constant percentage each time period, modelled as $y=a(1+r{)}^t$ for growth or $y=a(1-r{)}^t$ for decay, where $a$ is the starting value, $r$ the rate as a decimal, and $t$ time.

Linear change adds or subtracts the same fixed amount every period; exponential change multiplies by the same factor every period. A population growing by 50 people a year is linear. A population growing by 5% a year is exponential — and it accelerates over time in a way linear models never do.

Identify the starting amount, the percentage change per period, and whether the quantity increases (growth) or decreases (decay). Convert the percentage to a decimal, add it to 1 for growth or subtract from 1 for decay, then substitute into $y=a(1\pm r{)}^t$ with $t$ as the number of periods elapsed.

Half-life is the time it takes for a decaying quantity to reduce to exactly half its starting value — a special case of exponential decay where the decay factor is $0.5$ per half-life period rather than per year. It's used for radioactive substances, drug elimination in the body, and cooling problems.

It's assessed mainly under MYP Criterion A (Knowing and Understanding) and Criterion D (Applying Mathematics in Real-Life Contexts), through unit tests, investigations and sometimes a modelling task. According to the MYP: Mathematics guide, Criterion D tasks specifically require students to select and apply a mathematical model to an authentic, real-world scenario and justify its reasonableness.

Expect "calculate", "determine", "justify", "model" and "evaluate". "Calculate" wants a numeric answer with working shown; "justify" wants you to explain why your exponential model fits the data or context, not just state the answer — that's usually where Criterion D marks are lost.

Top marks come from combining an accurate model with genuine critical reflection: state your formula, show substitution clearly, then discuss the model's limits — does it hold for very large $t$, are there real-world constraints (a population can't grow forever), and how confident are you in the data used to build it?

Usually it's missing working, not the arithmetic. MYP criteria reward the process — showing the formula, the substituted values, and the reasoning — not just a correct number pulled from a calculator. Criterion A specifically checks for accurate use of mathematical language and clearly communicated steps, not just outcomes.

Extended MYP 4-5 Mathematics goes deeper into exponential functions — including deriving models from data, comparing growth rates, and connecting to logarithms — while Standard covers the basic formula and simple applications. Both pathways feed into DP Mathematics: Analysis and Approaches, where exponential and logarithmic functions return in far more depth.

Compound interest and loan repayments, population growth models in Individuals & Societies, radioactive half-life in Sciences, and even viral spread models students met during interdisciplinary units. Seeing the same formula reused across subjects is exactly the kind of cross-curricular thinking the MYP: From Principles into Practice guide asks teachers to build toward.

Both DP pathways build directly on this MYP work: Mathematics: Analysis and Approaches extends exponential functions into logarithms, continuous growth, and calculus of exponentials, while Mathematics: Applications and Interpretation focuses on modelling real data with exponential regression. Solid MYP foundations here make the DP jump far less steep.

The single most useful thing is making sure your child can explain, out loud, whether a scenario is growth or decay before touching a calculator — that judgment call is where most marks are actually lost, not the arithmetic. Past MYP-style questions and topical worksheets, like those on RevisionPrep, give repeated practice at spotting that distinction quickly.

Look for resources with worked, MYP-criteria-aligned examples rather than generic algebra drills — the MYP assessment style rewards justification and real-context modelling, not just calculation speed. RevisionPrep's Topical Worksheets and Revision Notes for MYP Mathematics are built around exactly this criterion-based format, with Criterion D-style tasks included.