A model that describes the association between the hours spent studying for an examand the mark achieved is: mark = 20 + 40 × log (hours) From this model, we would predict that a student who studies for 20 hours would scorea mark (to the nearest whole number) of:

Question

BlackTom AI · Accepted Answer

Using base-10 logarithms: log10(20) ≈ 1.30103. The model is mark = 20 + 40 × log(hours).

Step-by-step calculation:
1. Compute the logarithm (base 10) of 20: log10(20) = 1.30103 (approx).
2. Multiply by 40: 40 × 1.30103 = 52.0412.
3. Add 20: 20 + 52.0412 = 72.0412.
4. Round to the nearest whole number: 72.0412 → 72.

Why base-10 is used here: In many applied statistics and modelling contexts where "log" is written without a specified base, it commonly denotes the common (base-10) logarithm. Using ln (natural log) would give a different result (ln(20) ≈ 2.9957 → 20 + 40×2.9957 ≈ 139.83 → 140), which corresponds to option (a). Because the provided correct answer is 72, the intended interpretation must be log base 10.

Why the other options are incorrect:
- (a) 140 would result from using the natural logarithm (ln) instead of log10, so it does not match the conventional interpretation here.
- (c) 78 and (d) 80 do not match the computed value 72.0412; they would require log(hours) values of about 1.45 and 1.5 respectively (since 20 + 40×1.45 = 78, 20 + 40×1.5 = 80), which do not equal log10(20).

Conclusion: Interpreting log as base 10 and following the arithmetic yields a predicted mark of 72, which confirms the provided correct answer (b. 72).

A model that describes the association between the hours spent studying for an examand the mark achieved is: mark = 20 + 40 × log (hours) From this model, we would predict that a student who studies for 20 hours would scorea mark (to the nearest whole number) of:单项选择题

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