Question

3. The function represents the number of specialty items produced at the old factory w weeks after a change in management. The graph represents the number of specialty items produced at the new factory during the same time period.

(a) During Week 0, how many more specialty items were produced at the old factory than at the new factory? Explain.
(b) Find and compare the growth rates in the weekly number of specialty items produced at each factory. Show your work.
(c) When does the weekly number of specialty items produced at the new factory exceed the weekly number of specialty items produced at the old factory? Explain.

Answer 1

During week 0, there were 20 more specialty items produced at the old factory than at the new factory. To compare the growth rates, we can calculate the rate of change between consecutive weeks. When the value on the graph for the new factory exceeds the value for the old factory, the weekly number of specialty items produced at the new factory is higher.

Step-by-step explanation:

(a) During Week 0, the number of specialty items produced at the old factory was 20 more than at the new factory. We can determine this by looking at the graph and comparing the values of the old factory and the new factory at Week 0.

(b) To find and compare the growth rates in the weekly number of specialty items produced at each factory, we need to calculate the rate of change between consecutive weeks for both factories. We can use the formula:

Growth Rate = [(New value - Old value) / Old value] * 100%

(c) The weekly number of specialty items produced at the new factory exceeds the weekly number produced at the old factory when the value on the graph for the new factory is higher than the value for the old factory. We can find this by comparing the values on the graph for each week.