The function is:
W(x)=740× # 0.87 # ^x
This is an exponential decay function because the base 0.87is between 0 and 1:
0 < 0.87 < 1
That means the sample's weight decreases over time.
We need to find the weight when:
x=3
Substitute 3into the function:
W(3)=740× # 0.87 # ^3
First calculate the exponent:
# 0.87 # ^3=0.87×0.87×0.87
# 0.87 # ^3=0.658503
Now multiply by 740:
W(3)=740×0.658503
W(3)=487.29222
Rounded to two decimal places:
W(3)#487.29
So the weight of the radioactive sample after 3 years is approximately:
487.29 " oz. "

The graph shows P(t), where:
t= " years since opening "
and
P(t)= " daily profit in hundreds of dollars "
The graph is a downward-opening curve, so its maximum value occurs at the highest point of the graph, also called the vertex.
From the graph, the highest point occurs at approximately:
t=9
So the maximum daily profit happened approximately:
9 " years after opening "
The vertical value at this maximum point is approximately:
P(t)=29
But the graph measures profit in hundreds of dollars, so:
29×100=2900
Therefore, the maximum daily profit was approximately:
$2,900
So the correct interpretation is:
" Approximately 9 years after opening, a maximum daily profit of approximately " $2,900 " was earned. "

The graph shows a linear relationship between the amount of red dye, r, and the amount of yellow dye, y.
The rate of change of a line is the slope:
" slope " =( " change in " y)/( " change in " r)
From the graph, the line goes through the origin and rises steeply. A clear point on the line is approximately:
(2#9)
This means when the amount of red dye is 2gallons, the amount of yellow dye is 9gallons.
So the rate of change is:
9/2
That means for every 2gallons of red dye, the factory uses 9gallons of yellow dye.
The relationship can be written as:
y=9/2 r
So the correct interpretation is:
" The amount of yellow dye must be " 9/2 " of the amount of red dye. "
Therefore, the correct answer is:
# ( " A " )

The graph shows:
P(t)= " weekly profit in thousands of dollars "
where:
t= " years since opening "
The graph is a downward-opening curve, so it has a maximum value at its highest point. In Applied Algebra, the highest point of this kind of polynomial graph is called the vertex.
To answer the question, we need the t-value of the vertex because the question asks when the store had its maximum weekly profit.
From the graph, the highest point occurs between:
t=5
and
t=6
More specifically, it is approximately:
t=5.5
So the store had its maximum weekly profit approximately:
5.5 " years after opening "

The graph shows a decreasing exponential function.
In Applied Algebra, a decreasing exponential function may approach a fixed value over time. This fixed value is called the horizontal asymptote.
The horizontal asymptote represents the long-term value that the function gets closer and closer to, but does not necessarily cross or reach exactly.
From the graph, the curve decreases quickly at first, then begins to level off near:
y=1,000
This means that as time continues, the number of letters processed per day approaches:
1,000
So the long-term trend is that the mail center will process about:
1,000 " letters per day "