Exam Strategy

Readiness Check

You are ready when you can:

• Write $f(t)=ab^t$ from a verbal scenario with correct $a$, $b$, and units.
• Verify exponential fit with a constant ratio over equal steps.
• Solve for $a$ and $b$ from two points.
• Interpret $b$ as growth/decay factor and percent change.
• Rewrite models across time units and predict within domain.

On the AP Exam

• MCQ: pick the correct model, parameter, or prediction.
• FRQ: construct from data/context, show system or regression setup, interpret, predict.
• Skills: 1.C construct models (transformations/regression); 3.B apply numerical results in context.

Tactics

1. Identify multiplicative language: "factor of," "percent per," "doubles every." 2. $a=f(0)$ when the model starts at $t=0$ without shift. 3. Two points: $\dfrac{f(t_2)}{f(t_1)}=b^{t_2-t_1}$. 4. Percent growth $r$ per unit: $b=1+r$; decay: $b=1-r$. 5. Equivalent time units: $(b^{k})^{t/k}$. 6. State whether a prediction is interpolation or extrapolation.

Common Traps

• Linear model on exponential data.
• Forgetting baseline/asymptote in applied settings.
• Mis-scaled $b$ when the time unit changes.
• Unreasonable predictions outside context.

Quick Checklist

• [ ] Model form $ab^t$ (or $ae^{kt}$) stated with units
• [ ] $a$ and $b$ interpreted in context
• [ ] Prediction computed and justified
• [ ] Domain/limitations noted