https://file.aiquickdraw.com/mathbot/file/1727311129440jf4jxr8v.jpg

The question in the image asks about interpreting the structure of a linear expression representing the total amount of medicine Bailey has taken after \( d \) days. The expression is:

\[
10 + 0.2(d - 1)
\]

This represents the sum of 10 milligrams taken on the first day and 0.2 milligrams for each day after the first, hence for \( d - 1 \) days.

To break it down:
- The constant \( 10 \) represents the initial dose on the first day.
- The term \( 0.2(d - 1) \) represents the additional amount of medicine taken after the first day, where \( d \) is the total number of days.

Let's now match this understanding to the choices in the image:
1. **"It is the sum of the initial amount and the number of days, \( d \)"** – Incorrect. The expression involves adding the initial dose and the additional dose, not just the number of days.
2. **"It is the difference between the initial amount and the additional amount after \( d \) days"** – Incorrect. The expression adds, not subtracts, the initial amount and additional doses.
3. **"It is the sum of the initial amount and the additional amount after \( d \) days"** – Correct. This matches the structure of the expression where the total is the sum of the initial 10 milligrams and the additional dose over the following days.
4. **"It is the product of the initial amount and the additional amount after \( d \) days"** – Incorrect. There is no multiplication of the initial dose and the additional amount.

The correct answer is: **"It is the sum of the initial amount and the additional amount after \( d \) days."**

Would you like a further breakdown of this problem?

Here are some related questions for further practice:
1. How would the expression change if Bailey took 0.5 mg each day after the first day instead of 0.2 mg?
2. What does the expression \( 10 + 0.2d \) represent, and how is it different from \( 10 + 0.2(d - 1) \)?
3. How would you graph the expression \( 10 + 0.2(d - 1) \) for \( d \) values from 1 to 10?
4. What would the total amount of medication be after 5 days using the given expression?
5. Can you write a similar expression for a situation where Bailey takes 15 mg on the first day and 0.3 mg on each subsequent day?

**Tip**: When interpreting algebraic expressions, always break down each term to understand what it represents in the context of the problem.

Bailey receives medication and takes 10 milligrams the first day. He has to take 0.2 milligrams of the medicine each day for a number of days, d, after that. He writes the expression 10 + 0.2(d - 1) to find the total amount of medicine he has taken after d days. Which statement about his expression is true?

Solve a math problem where Bailey receives medication, takes 10 mg the first day, and 0.2 mg each day after. Learn how to interpret the linear expression 10 + 0.2(d - 1) to find the total dosage over d days. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation