Math Problem Statement

Based on the average amounts earned between the 5th and 10th year and between the 20th and 25th year, does it appear that the rate at which annual income increases is increasing or decreasing with time?

Solution

Based on the image you uploaded, the question asks about the rate at which annual income increases. Specifically:

  1. The average amount earned between the 5th and 10th year is $270.40 per year.
  2. The average amount earned between the 20th and 25th year is $492.6 per year.

The next part asks whether the rate at which annual income increases is increasing or decreasing.

Analysis:

  • Between the 5th and 10th year, the average earning is $270.40.
  • Between the 20th and 25th year, the average earning is $492.60.

Since the average amount earned per year has increased from $270.40 to $492.60, the rate at which annual income increases is increasing over time.

So, the correct choice would be "increasing".

Would you like more details or have any further questions?

Here are 5 related questions for deeper understanding:

  1. How can we calculate the exact rate of increase in income between two intervals?
  2. What factors could affect the change in income over time in a real-world scenario?
  3. How do linear and exponential growth models differ in explaining income growth?
  4. If the rate of increase continues, what would be the projected earnings after 30 years?
  5. How does compound interest relate to increasing rates of income over time?

Tip: Always compare data over multiple intervals to determine if the rate of change is consistent or accelerating.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Mean
Growth Rate

Formulas

(Total earnings over interval) / (Number of years in interval)

Theorems

Arithmetic Mean Theorem

Suitable Grade Level

Grades 9-12