Furniture Assembly: At the beginning of your 8 hour shift, there were 42 units of furniture that needed assembled. The number of units N that still need to be assembled during your shift can be modeled by n(t)=-3t +42 where t is the time in hours...
1. Graph the model
2. What is a reasonable domain and range of the model?
3. How many units still need to be assembled after you have worked 5 hours of your shift?
I think you can graph straight line
t = 0 to t = 8 (end of shift, you still have 18 left for the next shift :(
n = 42 to n =18
-3(5) + 42 = 27
Thankyou Mr.Damon :D
You are welcome.
To graph the given model n(t) = -3t + 42, we can use a Cartesian coordinate system with the horizontal axis representing time (t) in hours and the vertical axis representing the number of units to be assembled (n(t)).
1. Graphing the model:
- Choose a set of values for t (time) and substitute them into the equation to find the corresponding values of n(t) (number of units).
- Plot the points on the graph, connecting them to show the trend.
Here is the graph of the model:
^
|
42 | .
| .
| .
| .
| .
| .
------------------------------>
0 5 10
2. Reasonable domain and range of the model:
The domain represents the set of possible inputs, which is the time in hours (t). In this case, a reasonable domain would be all non-negative real numbers since time cannot be negative in this context. So, the domain is t ≥ 0.
The range represents the possible outputs, which is the number of units to be assembled (n(t)). Looking at the equation, we can see that as time increases, the number of units will decrease. Since you can't have a negative number of units to be assembled, a reasonable range would be all non-negative real numbers. So, the range is n(t) ≥ 0.
3. To find the number of units still needing assembly after 5 hours of your shift, we can substitute t = 5 into the equation:
n(t) = -3t + 42
n(5) = -3(5) + 42
n(5) = -15 + 42
n(5) = 27
Therefore, after working for 5 hours, there will still be 27 units that need to be assembled.