\(\mathrm{s(d) = 0.1d + 4.8}\)The given function s models the amount of money, in dollars, saved in a piggy bank...

1. TRANSLATE the problem information

• Given: \(\mathrm{s(d) = 0.1d + 4.8}\) models dollars saved after d days
• Find: How many cents are saved each day

2. INFER what we need from the function

• This is a linear function in the form \(\mathrm{y = mx + b}\)
• The coefficient of d (which is 0.1) is the slope
• Slope represents the rate of change - how much s increases for each 1-unit increase in d
• So 0.1 represents dollars saved per day

3. SIMPLIFY the unit conversion

• Daily savings = 0.1 dollars per day
• Convert to cents: \(\mathrm{0.1 \text{ dollars} \times 100 \text{ cents/dollar} = 10 \text{ cents per day}}\)

Answer: A (10)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students focus on the y-intercept (4.8) instead of the slope (0.1)

They might think "4.8 appears in the function, so maybe that's related to daily savings" and select 48 cents (choice B) or get confused about the units. The y-intercept represents the initial amount already in the piggy bank, not the daily rate.

This may lead them to select Choice B (48).

Second Most Common Error:

Missing unit conversion: Students correctly identify that 0.1 is the daily rate but forget to convert from dollars to cents

They stop at "0.1 per day" and might select choice C (1) thinking it's close, or get confused about what the 0.1 represents in terms of cents.

This may lead them to select Choice C (1).

The Bottom Line:

This problem tests whether students understand that in a linear function, the coefficient of the variable represents the rate of change, and whether they can properly convert between units.