Exponential Function Context and Data Modeling
▶︎ Watch it animatedinteractive step-through · ~3 min · optionalAn exponential model is two committed choices: the initial value a out front, and the per-unit factor b in the base. Contexts encode them in percent language (6% growth means b = 1.06, 6% loss means b = 0.94), in doubling times and half-lives (equal factors over equal intervals), or in data pairs, where dividing two outputs cancels a and exposes the factor over the gap between inputs.
The mistakes are translations gone wrong: treating percent growth as a flat amount added each step, planting the rate where the factor belongs (0.06 as a base), reading the base as 106% growth, or swapping which parameter starts and which one multiplies. Each translation error is named and drilled in the lesson.
The work
3 ways in · any order
Lesson
Exponential Function Context and Data Modeling
›
From story to model: the lesson drills the two decisions behind a times b to the x, converting percent language to factors, counting doubling intervals rather than units, and fitting both parameters from data by division. Ten scenarios close it out, all built on the translations students actually get wrong.
Diagnostic
10-item topic check
›
Ten items spanning the three Topic 2.5 misconceptions: percent growth treated as flat addition, growth rates planted where factors belong, and initial value swapped with the base. Results route you to the drills that fix what fired.
Targeted Practice
Drill a single misconception
›
Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears it for now and moves you to the next. Two in a row is a checkpoint, not proof: if the error resurfaces later, the misconception comes back.