For the years 1972-2007, Total World Credit Market Debt (TWCMD), as me

For the years 1972-2007, Total World Credit Market Debt (TWCMD), as measured in trillions of US dollars, is accurately modeled by the equation \(y = N • 2^{k(t - 1972)}\), 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.

The constant N is approximately equal to

We can determine N by looking at the value of TWCMD in 1972 since, in 1972, \(t - 1972 = 0\), so \(2^{k(t - 1972)} = 1\). Thus, in 1972, \(y = N\).

In 1972, TWCMD appears to be around 3.

Select 3.

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

Since TWCMD \(= y = N • 2^{k(t - 1972)}\), TWCMD will double each time \(k(t - 1972)\) increases by \(1\). After all, each time \(k(t - 1972)\) increases by \(1\), \(2^{k(t - 1972)}\) increases by a power of 2, and thus \(y\) doubles.

Looking at the graph, we see that y doubles from 5 to 10 and from 10 to 20 in approximately 9 years in each case. So, it takes 9 years for \(k(t - 1972)\) to increase by \(1\).

If the model continues to be accurate, we can expect this pattern to hold after 2007.

So, it will take another approximately 9 years for TWCMD to double from its level in 2007.

Select 2016.

Correct Answer