Quick questions on Exponential growth and decay applications (QCE Math Methods Unit 2)

$y = A r^t$ where: - $A$ is the initial value at $t = 0$. - $r$ is the per-time-unit multiplier. - $r > 1$ for growth, $0 < r < 1$ for decay.

$y = A e^{kt}$ where: - $A$ is initial value. - $k$ is the continuous growth rate ($k > 0$ growth, $k < 0$ decay). - Used when growth is compounded continuously (continuously compounded interest, radioactive decay in mathematically clean form).

$A$ is the initial value, not the value at the time being asked about.

$r$ is a growth factor (a number near $1$), not the percentage. A $5\%$ annual growth means $r = 1.05$.

A decay model with $r > 1$ models growth, not decay.

If $r$ is per year, $t$ must be in years. If you switch units, recompute $r$.

Building a discrete model from a scenario and predicting a value at a stated time.

Multiple choice on identifying the growth factor or the doubling time.

A multi-part contextual problem: build the model, predict a value, solve for the time at which a target is met. Often combined with calculus in Year 12 to find an instantaneous rate of change.