Grisham is considering the three situations below.

I. For the first 28 days, a sunflower grows at a rate of 3.5 cm per day.

II. The value of a car depreciates at a rate of 15% per year after it is purchased.

III. The amount of bacteria in a culture triples every 2 days during an experiment.

Which of the statements describe a situation with a equal difference over an equal interval?

(1) I, only
(2) II, only
(3) I and III
(4) II and III

I don't understand what it means by "equal difference over an equal interval".

"Equal difference over an equal interval" refers to a situation where the change or difference in a certain quantity remains consistent or constant over a specific interval of time.

Let's analyze the three situations described:

I. For the first 28 days, a sunflower grows at a rate of 3.5 cm per day.

In this scenario, the sunflower is growing at a constant rate of 3.5 cm per day. Therefore, the difference in growth (3.5 cm) remains equal throughout the 28-day interval.

II. The value of a car depreciates at a rate of 15% per year after it is purchased.

In this case, the car's value depreciates at a fixed rate of 15% per year. However, the term "equal interval" is not applicable here since the depreciation is measured over a yearly interval, not a specific, equal interval.

III. The amount of bacteria in a culture triples every 2 days during an experiment.

In this scenario, the amount of bacteria triples every 2 days. While the amount is changing, the difference of tripling remains consistent over the 2-day interval.

Based on the analysis, only situations I and III describe a situation with an equal difference over an equal interval. So the correct answer is (3) I and III.

"Equal difference over an equal interval" means that the change in value or quantity remains constant over a fixed period of time. In other words, there is a consistent rate of change.

Let's examine each situation to see if they fit this description:

I. For the first 28 days, a sunflower grows at a rate of 3.5 cm per day.

In this scenario, the sunflower grows at a constant rate of 3.5 cm per day. The difference in growth (3.5 cm) remains the same over each daily interval. So, this situation has an equal difference (3.5 cm) over an equal interval (1 day).

II. The value of a car depreciates at a rate of 15% per year after it is purchased.

Here, the car's value decreases by 15% each year. While the percentage loss is constant, the interval is not specified. It could be any specific year or a range of years. Without an equal interval mentioned, we cannot determine if there is an equal difference over an equal interval.

III. The amount of bacteria in a culture triples every 2 days during an experiment.

In this case, the amount of bacteria in the culture triples every 2 days, which means it grows exponentially. The rate of change is not constant, as it depends on the previous amount of bacteria. Therefore, there is no equal difference over an equal interval.

Based on the explanations above, we can conclude that only situation I fits the criteria of having an equal difference over an equal interval. So, the correct answer is (1) I, only.

it means that the change does not depend on the amount already present. The amount changes by a constant amount each time period. That is, a fixed amount per year, per day, etc.

So, what do you think?