Set up, solve and interpret the answers in growth and decay problems,…

Growth and decay problems describe repeated percentage change from an initial amount. Compound interest is one financial example. The key idea is that each period applies the same multiplier to the previous amount, not to the original amount only. Before we calculate, think about whether the amount is increasing or decreasing. For growth, the multiplier is one plus r, where r is the rate written as a decimal. For decay, the multiplier is one minus r. After n periods, the amount is the initial amount times the multiplier to the power n. For example, a growth rate of four percent has multiplier one point zero four; a decay rate of four percent has multiplier zero point nine six. First identify the initial amount, the rate as a decimal, and the number of periods from the wording. Next choose one plus r for growth or one minus r for decay. Then form initial times multiplier to the power n and evaluate it accurately. Keep full accuracy until the final answer, then round and include units as the problem requires. Check whether the question asks for the final amount, the interest earned, or the number of periods. Here is a worked example. Five hundred pounds is invested at four percent compound interest for three years. The initial amount is five hundred, the multiplier is one point zero four, and n is three. Before I show the evaluation, pause and decide what expression to use. The expression is five hundred times one point zero four cubed. Evaluating gives five hundred sixty-two point four three two, which is five hundred sixty-two pounds and forty-three pence to the nearest penny. A common mistake is using the rate as a whole number, such as multiplying by four instead of one point zero four. Convert the percentage to a decimal and add one for growth. Another mistake is using simple interest, which adds the same amount each period, instead of multiplying by the multiplier each period. For decay, use one minus r, not one plus r. Also avoid rounding too early in a multi-step calculation. To summarise, set up repeated percentage change as initial times multiplier to the power n. Use one plus r for growth and one minus r for decay, and distinguish compound interest from simple interest. Interpret the final value in context, with suitable units and rounding. At Higher tier, if the final amount and rate are known, you may need to find n by trial and improvement. Check exactly what the question asks you to answer.