Exponential and logarithmic evidence: mixed practice
Bring ideas together without being told which method to use. Show the reasoning that makes your result valid.
Suggested session length: 50 minutes, as an unvalidated planning estimate. This collection contains 3 tasks; choose a manageable set and return for further sessions. Completing the whole collection may take substantially longer. This is a unit assessment, not a full course or AP examination.
Show assumptions, units, domain restrictions and intermediate calculations.
Keep new observations separate from fitting and retain the tool equation, residual evidence and transformation.
Written solutions require rubric review; practice completion is not certification.
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0 of 3 tasks have recorded responses. No overall mastery score is assigned.
A synthetic sensor reads 52,28,16 at t=0,2,4 minutes. Assume a nonconstant shifted exponential and recover its rule. Predict at 6 minutes before inspecting a fresh reading 10.15±0.1. Assess the check and rewrite the rule in elapsed seconds.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
Use the logarithmic fitting tool on pairs (1,12.1),(3,9.8),(9,8.2),(27,5.9), with response in points. Record coefficients in a stated logarithm base, residuals and original-scale SSE. Predict at √3 before comparing fresh output 11.0. Then express the fitted-model input producing response 8 and distinguish it from an independently verified target. Tolerance 0.002 for coefficients in base 3, SSE and prediction.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
For f(x)=6−2·(1/2)^(3x), restricted to x≥0, derive its inverse and exact domain/range pairs. Solve log_(1/2)((6−y)/2)≤−3 directly with domain conditions and interpret the result as a restriction on the original input.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
Review and revisit
Use each rubric to identify a valid argument, a missing condition or a step to revise. For independent evaluation, ask a teacher or reviewer to examine the complete reasoning. Self-review and recorded responses are not verified assessment results.
Coverage and targeted lesson returns
A synthetic sensor reads 52,28,16 at t=0,2,4 minutes. Assume a nonconstant shifted exponential and recover its rule. Predict at 6 minutes before inspecting a fresh reading 10.15±0.1. Assess the check and rewrite the rule in elapsed seconds.
Use the logarithmic fitting tool on pairs (1,12.1),(3,9.8),(9,8.2),(27,5.9), with response in points. Record coefficients in a stated logarithm base, residuals and original-scale SSE. Predict at √3 before comparing fresh output 11.0. Then express the fitted-model input producing response 8 and distinguish it from an independently verified target. Tolerance 0.002 for coefficients in base 3, SSE and prediction.
For f(x)=6−2·(1/2)^(3x), restricted to x≥0, derive its inverse and exact domain/range pairs. Solve log_(1/2)((6−y)/2)≤−3 directly with domain conditions and interpret the result as a restriction on the original input.
