Question

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.

During week 0 how many more specialty items were produced at the old factory than at the new factory. Explain.

Answer 1

During week 0, there were 70 more specialty items produced at the old factory than at the new factory.

Step-by-step explanation:

To find the number of specialty items produced at the old factory during week 0, we need to evaluate the function p(w) = 70w + 320 when w = 0:

p(0) = 70(0) + 320 = 0 + 320 = 320

So, during week 0, the old factory produced 320 specialty items.

To find the number of specialty items produced at the new factory during week 0, we need to evaluate the function n(w) = 250 * 1.25^w when w = 0:

n(0) = 250 * 1.25^0 = 250 * 1 = 250

So, during week 0, the new factory produced 250 specialty items.

To find how many more specialty items were produced at the old factory than at the new factory during week 0, we subtract the number of specialty items produced at the new factory from the number produced at the old factory: 320 - 250 = 70.

Therefore, during week 0, there were 70 more specialty items produced at the old factory than at the new factory.