Final answer:
To notice a difference in sweetness with 10 teaspoons of sugar already in coffee, one must add 2 teaspoons of sugar, calculated using the proportion of increase perceived with an initial amount of 5 teaspoons.
Step-by-step explanation:
The student's question relates to the concept of just noticeable difference (JND), which in this case, is applied to the sweetness of coffee as perceived by a change in the amount of sugar added. To calculate the additional amount of sugar needed to notice a difference in sweetness, we can use the initial scenario: a change from 5 to 6 teaspoons of sugar was enough to notice a difference. Assuming the difference is proportional, and the student wants to notice at least half the time, it's suggested that the proportional amount of sugar needs to be added.
To find the proportional amount to add to 10 teaspoons based on the original case, we use the following steps:
- Find the proportion of the increase: 1 teaspoon increase on 5 teaspoons of original amount, which is \( \frac{1}{5} = 0.2 \) (or 20%).
- Apply this proportion to the new amount of 10 teaspoons: \( 10 teaspoons \times 0.2 = 2 teaspoons \).
Therefore, to notice a difference in sweetness at least half the time with 10 teaspoons of sugar already in the coffee, you would need to add 2 teaspoons of sugar.