The Seneca Children's Fund (SCF) is a local charity that runs a summer camp for disadvantaged children. The fund's board of directors has been working very hard in recent years to decrease the amount of overhead expenses, a major factor in how charities are rated by independent agencies. The following data show the percentage of the money SCF has raised that was spent on administrative and fund-raising expenses for a seven-year period.

Year	Period (t)	Expense (%)
1	1	14.0
2	2	12.1
3	3	10.4
4	4	10.4
5	5	11.6
6	6	10.1
7	7	8.4

(a)Construct a time series plot.

A time series plot contains a series of 7 points connected by line segments. The horizontal axis ranges from 0 to 8 and is labeled: Time Period (t). The vertical axis ranges from 0 to 16 and is labeled: Expense (%). The points are plotted from left to right in a fairly consistent downward, diagonal direction at regular increments of 1 period starting at period 1. The points are between 6 to 12 on the vertical axis.

A time series plot contains a series of 7 points connected by line segments. The horizontal axis ranges from 0 to 8 and is labeled: Time Period (t). The vertical axis ranges from 0 to 16 and is labeled: Expense (%). The points are plotted from left to right in a fairly consistent upward, diagonal direction at regular increments of 1 period starting at period 1. The points are between 8 to 14 on the vertical axis.

A time series plot contains a series of 7 points connected by line segments. The horizontal axis ranges from 0 to 8 and is labeled: Time Period (t). The vertical axis ranges from 0 to 16 and is labeled: Expense (%). The points are plotted from left to right in a fairly consistent downward, diagonal direction at regular increments of 1 period starting at period 1. The points are between 8 to 14 on the vertical axis.

A time series plot contains a series of 7 points connected by line segments. The horizontal axis ranges from 0 to 8 and is labeled: Time Period (t). The vertical axis ranges from 0 to 16 and is labeled: Expense (%). The points are plotted from left to right in a fairly consistent upward, diagonal direction at regular increments of 1 period starting at period 1. The points are between 6 to 12 on the vertical axis.

What type of pattern exists in the data?

The time series plot shows a downward linear trend.

The time series plot shows an exponential trend.

The time series plot shows an upward linear trend.

The time series plot shows a quadratic trend.

(b)Develop the linear trend equation for this time series to forecast expense percentage.

T_t=

(c)Forecast the percentage of administrative expenses for year 8.

%

(d)If SCF can maintain their current trend in reducing administrative expenses, during which period will they first achieve a level of 5% or less?

Expenses will first reach a level of 5% or less in period _____.