Question

The function p(w)=238(1.6)^w 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? Show all work to receive full credit for this problem.
(b) Find and compare the growth rates of specialty items produced at each factory between weeks two and three. Show all work to receive full credit for this problem.
(c) Does the weekly number of specialty items produced at the new factory exceed the weekly number of specialty items produced at the old factory in week 5? Show all work to receive full credit for this problem.
mber of specialty items produced at the new factory during the same time period.

Answer 1

a.) w = 0

Old factory: $p(w)=238(1.6)^w$        Plug in 0

$p(0)=238(1.6)^0$        

When a number has an exponent of 0, the number becomes 1

p(0) = 238(1)

p(0) = 238

New factory: w = 0, p(0) or y = 190         (0,190)

238 - 190 = 48

During Week 0, 48 more specialty items were produced at the old factory than at the new factory.

Sorry I don't know how to do b or c