A town's population is 18,000 and grows by 2.8% each year. When will it first exceed 25,000?
Reasoning strategy
Set up an exponential inequality and solve or test whole years.
Difficulty Practice Guide
Hard Grade 10 Exponential & Logarithmic Models Word Problems
This page shows what hard practice should demand for grade 10 exponential & logarithmic models word problems. The goal is not a larger worksheet. The goal is to make the student's reasoning visible enough to choose the next better problem.
What Changes At This Difficulty
Stress-test transfer: multi-step structure, constraints, distractors, or reverse reasoning.
Expected structure: 3-4 step problem solving.
Vocabulary load: high with intentional distractors.
Reasoning depth: at least 3 relationship layers.
Student Work Signals
A good hard problem should expose the bottleneck
MathRoutine watches for whether the student understood the situation, wrote a useful setup, handled the calculation, and answered the exact question asked.
1
model hidden constraints or changed quantities
2
avoid tempting but incomplete first answers
3
explain why the final answer fits the original context
Sample Problems
A lab sample starts at 920 grams and loses 12% of its mass each hour. How much remains after 7 hours?
Reasoning strategy
Use a decay factor of 0.88 for each hour.
Why This Matters
The paid value is diagnosis, not answer lookup
Basic gives repeated targeted practice. Pro becomes useful when the student needs help understanding wording, recovering the setup, or seeing the same misconception return across attempts.
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