To determine when the weekly number of specialty items produced at the new factory exceeds the weekly number produced at the old factory, we set up an equation and solve for the value of w. The solution is obtained by creating a table of values and finding the point of intersection. The new factory's production exceeds the old factory's production for 4 weeks.
In order to determine when the weekly number of specialty items produced at the new factory exceeds the weekly number produced at the old factory, we need to set up an equation and solve for the value of w.
The equation is: n(w) = p(w)
Substituting the given functions, we have: 250 * 1.25^w = 70w + 320
To solve this equation, we can create a table of values, substituting different values of w and evaluating n(w) and p(w) at each value.
Here is the table:
w n(w) p(w)
0 250 320
1 312.5 390
2 390.625 460
3 488.28125 530
4 610.35156 600
From the table, we can see that the weekly number of specialty items produced at the new factory exceeds the weekly number produced at the old factory when w = 4. This means that it will last for 4 weeks.
The probable question may be:
The function n(w)=250 1.25^w represents the number of specialty items produced a the new factory w weeks after a change in management. The function p(w) = 70w +
320 represents the number of specialty items produced at the old factory in w weeks.
When does the weekly number of specialty items produced at the new factory exceed the weekly number of specialty i teams produced at the old factory. Explain how long this will last and use a table to show your work.