High School

The data in the table shows that the percentage of adults in a country who are currently married is declining. Assuming that the percentage of adults who are married will continue to decrease according to the exponential decay model:

| Year | Percent of Adults Who Are Married |
|------|----------------------------------|
| 1960 | 73.6 |
| 1980 | 67.7 |
| 2000 | 57.3 |
| 2010 | 51.7 |
| 2012 | 48.6 |

a) Use the data for 1960 and 2012 to find the value of \( k \).

Answer :

To find the value of k using the exponential decay model with the provided data for 1960 and 2012.

a) Use the data for 1960 and 2012 to find the value of k.

  1. Calculate the ratio of the percent of adults who are married in 2012 compared to 1960: 48.6% / 73.6%
  2. Use the exponential decay formula: P = P0 * e^(-kt), where P is the percentage in 2012, P0 is the percentage in 1960, e is the base of the natural logarithm, k is the decay rate, and t is the time difference.
  3. Substitute the values into the formula and solve for k to find the value.

Other Questions