The graph shows a decreasing exponential function.
The vertical axis represents:
" Letters per day "
The horizontal axis represents:
" Time in years "
For an exponential decay graph, the value decreases quickly at first and then begins to level off. The value it approaches in the long run is called the horizontal asymptote.
From the graph, the curve levels off near:
y=2,500
So the number of letters processed per day is trending toward:
2,500
This does not mean the mail center immediately processes exactly 2,500 letters per day. It means that as time continues, the number gets closer and closer to 2,500.
Therefore, the correct answer is:
# ( " B " )

The function is:
f(x)=190× # 0.99 # ^x
Since xrepresents the number of years since 2003:
2012 # x=9
2015 # x=12
The average rate of change from 2012 to 2015 is:
(f(12)-f(9))/(12-9)
First, find f(9):
f(9)=190× # 0.99 # ^9
f(9)#173.59
Now find f(12):
f(12)=190× # 0.99 # ^12
f(12)#168.37
Now calculate the average rate of change:
(168.37-173.59)/(12-9)
=(-5.22)/3
#-1.74
Rounded to the nearest whole number:
-2
The negative sign means the number of subscribers is decreasing.
So the correct interpretation is:
" The number of subscribers decreases at an average rate of about 2 subscribers per year. "

The value r^2measures how well a regression model fits the data.
Here:
r^2=0.25
This is a low r^2value, meaning the model explains only about:
25%
of the variation in the data.
That indicates a weak fit. When a model has a weak fit, using it for extrapolation is not reliable because predictions outside the data range may be very inaccurate.
Since:
0.25 < 0.3
the best conclusion is that extrapolation is not appropriate because the regression model does not fit the data well enough.
Therefore, the correct answer is:
# ( " C " )

The problem states that the greatest number of trees are sold when the temperature is over 70°F. Therefore, we need to identify the days on the graph when tree sales are highest. The graph shows two major peaks in the number of trees sold per day. These peaks occur around day 2 and day 10. Since higher tree sales are linked to temperatures over 70°F, those two days are the most likely days when the temperature exceeded 70°F. Day 6 appears near a low point, so it is not likely associated with high temperature based on the given relationship.
Day 12 also does not match the main peaks. Therefore, the correct answer is C.

The average daily change is the average rate of change over the interval from day 16 to day 20. From the graph, the performance score at day 16 is approximately 30.1, and the score at day 20 is approximately 57.6.
Use the formula
x
2
#x
1
y
2
#y
1
Substituting gives
20#16
57.6#30.1
The numerator is 27.5, and the denominator is 4, so the average daily change is 27.5/4=6.875, which rounds to 6.88. This means the performance score increased by an average of about 6.88 points per day over the interval. Therefore, the correct answer is B.