Write the equation for the following situation: In one U.S. town, the annual consumption, s, of sugar (in kg per person) can be estimated by adding 30 to half the years, t, since 1975.
Then graph the equation and use the graph to determine the sugar consumption in the year 1991.
"adding 30 to half the years, t, since 1975"
"years since 1975" => t=Y-1975
"add 30" => t+30 => 30+(Y-1975)
So
s(Y)=30+(Y-1975)
s(Y) = sugar consumption per person per year in kg
Y=year
The question requires the calculation of s(1991).
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To write the equation for this situation, we can break it down into two components: the constant term and the linear term.
1. Constant term: The constant term in this equation is 30, which represents the baseline annual sugar consumption in kg per person.
2. Linear term: The linear term in this equation is half the years since 1975, denoted as t/2. This term increases as the years since 1975 increase, indicating a linear relationship between time and sugar consumption.
Combining these two terms, the equation for the annual sugar consumption (s) in kg per person can be written as:
s = 30 + (t/2)
To determine the sugar consumption in the year 1991, we need to substitute the value of t (years since 1975) with the corresponding value for the year 1991. To do this, we calculate the years since 1975 by subtracting 1975 from 1991:
t = 1991 - 1975 = 16
Now we can substitute this value into our equation:
s = 30 + (16/2)
s = 30 + 8
s = 38
Therefore, the estimated sugar consumption in the year 1991 would be 38 kg per person.
To graph this equation, we can plot points representing different years since 1975 and corresponding sugar consumption values. The x-axis represents the years since 1975 (t) and the y-axis represents the sugar consumption (s). Since the equation is linear, we only need two points to draw a line.
For example, let's take two values for t: t=0 (representing the year 1975) and t=16 (representing the year 1991). Putting these values into the equation, we get:
For t=0:
s = 30 + (0/2)
s = 30
For t=16:
s = 30 + (16/2)
s = 30 + 8
s = 38
Now, we can plot the points (0, 30) and (16, 38) on the graph and draw a straight line passing through these two points as it represents the sugar consumption over time.
The graph would show that sugar consumption starts at a baseline of 30 kg per person in the year 1975 and increases linearly with time.
Note: In the graph, the x-axis represents the years since 1975, and the y-axis represents the annual sugar consumption (s) in kg per person.