For the years 1972-2007, Total World Credit Market Debt (TWCMD), as measured in trillions of US dollars, is accurately modeled...
GMAT Graphics Interpretation : (GI) Questions
For the years 1972-2007, Total World Credit Market Debt (TWCMD), as measured in trillions of US dollars, is accurately modeled by the equation \(y = N \cdot 2^{k(t - 1972)}\), whose graph is given. Here, N and k are positive constants and t denotes the year. From each drop-down menu, select the option that creates the most accurate statement based on the information provided.
Owning the Dataset
Table 1: Text Analysis
| Text Component | Literal Content | Simple Interpretation |
|---|---|---|
| Time Period | For the years 1972-2007 | Data covers a 35-year span from 1972 to 2007 |
| Subject | Total World Credit Market Debt (TWCMD) | Focus is on global credit market debt |
| Units | as measured in trillions of US dollars | All amounts are in trillions of US dollars |
| Model Description | is accurately modeled by the equation \(\mathrm{y = N \cdot 2^{k(t - 1972)}}\) | An exponential model predicts the debt growth |
| Parameters | N and k are positive constants and t denotes the year | N and k are constants; t is the year |
| Reference to Chart | whose graph is given | A graph visually presents the debt model |
Table 2: Chart Analysis
| Chart Component | What's Shown | What This Indicates |
|---|---|---|
| Chart Type | Line graph of TWCMD from 1972 to 2007 | Depicts how global debt has grown over 35 years |
| X-axis | Years (1972–2007, at 5-year intervals) | Shows temporal progression of the data |
| Y-axis | Debt (trillions of US dollars), ranging from ~0 to 45 | Illustrates scale and allows reading of values at each point |
| Data Points | 3 (1972), 4 (1977), 6 (1982), 9 (1987), ..., 43 (2007) | Exact TWCMD at select years; matches model |
| Growth Pattern | Smooth, increasingly steep upward curve | Indicates an exponential (not linear) growth—confirms the model |
| Model Match | Chart overlays equation \(\mathrm{y = N \cdot 2^{k(t - 1972)}}\) | Visual fit between real data and exponential model |
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.
- Key Phrase: The constant 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.
- Key Phrase: is approximately equal to
- 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.
- Calculations Estimations:
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.
- Key Phrase: If the model continues to be accurate beyond 2007
- 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.
- Key Phrase: the TWCMD will equal approximately double the 2007 value
- 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.
- Calculations Estimations:
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.