For the years 1972-2007, Total World Credit Market Debt (TWCMD), as measured in trillions of US dollars, is accurately modeled...

Owning the Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

The exponential equation uses N = 3, representing the 1972 debt value in trillions. The chart shows TWCMD increased from 3 to 43 trillion from 1972 to 2007, confirming exponential (not linear) growth—doubling roughly every 9–10 years. This model illustrates how global credit debt expands rapidly in compounding fashion with time.

Step-by-Step Solution

Question 1: Determining the Value of the Constant N in the Exponential Model

Complete Statement:

The constant N is approximately equal to _____

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: The constant N
    • Meaning: Refers to the starting value of the model, defined as \(\mathrm{y = N \cdot 2^{k(t - 1972)}}\).
    • Relation to Chart: Corresponds to the TWCMD value at t = 1972.
    • Important Implications: To find N, set t = 1972; the equation simplifies to y = N.
• Statement Breakdown 2:
  • Key Phrase: is approximately equal to
    • Meaning: Indicates we can use an estimate from the provided chart.
    • Relation to Chart: Requires using the chart's value for TWCMD in 1972.
    • Important Implications: Interpreting the value in trillions of US dollars and matching to one of the provided choices.
• What is needed: The initial value of TWCMD (in trillions of US dollars) in the year 1972.

Solution:

• Condensed Solution Implementation:
  Look at the chart for t = 1972 to find TWCMD and equate this to N.
• Necessary Data points:
  TWCMD in 1972 as shown on the chart: 3 trillion US dollars.
  • Calculations Estimations:
    Substitute t = 1972 into the model: \(\mathrm{y = N \cdot 2^{k(1972-1972)} = N \cdot 1 = N}\). Thus, N = 3.
  • Comparison to Answer Choices:
    Choices are 0, 1, 3, 6, and 10. 3 is the correct value.

FINAL ANSWER Blank 1: 3

Question 2: Predicting When TWCMD Will Double the 2007 Value

Complete Statement:

If the model continues to be accurate beyond 2007, the TWCMD will equal approximately double the 2007 value in the year _____

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: If the model continues to be accurate beyond 2007
    • Meaning: We extend the exponential model into the future, past the data shown.
    • Relation to Chart: We use the past pattern in the data to make a future prediction.
• Statement Breakdown 2:
  • Key Phrase: the TWCMD will equal approximately double the 2007 value
    • Meaning: We look for the year in which TWCMD reaches \(\mathrm{2 \times 43 = 86}\) trillion.
    • Relation to Chart: 2007 value from chart is 43 trillion; we're looking for when it'll reach 86 trillion.
• What is needed: The year when TWCMD will reach approximately 86 trillion (double the 2007 value).

Solution:

• Condensed Solution Implementation:
  Observe the doubling pattern in the chart and add a doubling period to 2007.
• Necessary Data points:
  TWCMD in 2007 = 43 trillion. Prior doublings: 3 (1972) → 6 (1982) (~10 yrs), 20 (1997) → 43 (2007) (~10 yrs).
  • Calculations Estimations:
    Doubling time is roughly 9-10 years. 2007 + 9 ≈ 2016.
  • Comparison to Answer Choices:
    Of 2016, 2025, 2034, the closest is 2016.

FINAL ANSWER Blank 2: 2016

Summary

To solve the first blank, we recognize that N is the initial value in the exponential model at t = 1972, which the chart gives as 3 trillion. To solve the second blank, we observe the pattern that the value roughly doubles every 9-10 years, so starting from 43 trillion in 2007, it should reach 86 trillion around 2016.

Question Independence Analysis

These questions are independent: finding N in question 1 relies only on the value at t=1972, while question 2 requires identifying and applying the growth pattern beyond 2007. Solving one does not depend on the answer to the other.