This question asks us to compare the heights of two balls at a specific time:
t=0.9
The graph shows:
Ball 1 as the solid blue curve.
Ball 2 as the dashed blue curve.
To determine which ball was lower at t=0.9, we look at the vertical positions of both curves when the time is
0.9seconds.
At approximately t=0.9:
" height of Ball 1 " < " height of Ball 2 "
This means Ball 1 is lower than Ball 2 at that time.
The correct reasoning must say both:
Ball 1 was lower, and
Ball 1's height was less than Ball 2's height at t=0.9.
That matches option A.

Since xrepresents the number of years since 2003:
2003 # x=0
2007 # x=4
The average rate of change from 2003 to 2007 is:
(f(4)-f(0))/(4-0)
Find f(0):
f(0)=280× # 1.08 # ^0
f(0)=280
Find f(4):
f(4)=280× # 1.08 # ^4
f(4)#380.94
Now calculate:
(380.94-280)/4
=100.94/4
#25.23
Rounded to the nearest whole number:
25
Since the value is positive, the number of subscribers is increasing.
So the correct interpretation is:
" The number of subscribers increases at an average rate of 25 subscribers per year. " Therefore, the correct answer is:
# ( " C " )

This question asks us to interpret unusually high values on a graph. The problem states that more customer accounts are opened during snowy weeks than during weeks without snow. Therefore, the likely snowy weeks correspond to the peaks on the graph, where the number of new customer accounts is noticeably higher than surrounding weeks. The graph shows clear spikes at approximately week 7 and week 14. These weeks have higher account openings compared with nearby weeks, making them the best evidence of snowy conditions.
Week 1 and week 5 do not match the main peaks shown in the graph. Since the snowy weeks should correspond to the highest customer-account values, the correct answer is D.

This graph represents a logistic growth function, which has an S-shaped curve:
Slow growth at the beginning (near point A)
Rapid growth in the middle (near point B and C)
Slowing growth at the end (near point D)
Key Concept:
Instantaneous rate of change = slope of the tangent line at a single point Average rate of change = slope between two points Analyze the graph:
At point A # slope is small (slow increase)
From A to C # increasing but not maximum
At point C # curve is steepest # maximum slope
From C to D # curve flattens # smaller slope
At point D # slope is very small (almost flat)
Conclusion:
The greatest rate of change occurs where the graph is steepest, which is at:
" Point C "

Since xrepresents the number of years since 2004:
2013-2004=9
so:
2013 # x=9
Also:
2018-2004=14
so:
2018 # x=14
The average yearly rate of change from 2013 to 2018 is:
(f(14)-f(9))/(14-9)
Now evaluate the function:
f(9)=330× # 1.04 # ^9
f(9)#469.37
f(14)=330× # 1.04 # ^14
f(14)#571.13
Now calculate the average rate of change:
(571.13-469.37)/5
=101.76/5
=20.35
So the painting's value increased by an average of about:
$20.35 " per year "
Therefore, the correct answer is:
# ( " A " )