The function p(w)=230(1.1)^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? 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.

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Step-by-step explanation:

answer:   a) 40 items.

b) in old factory, growth rate is 0.1 or 10%

in new factory, growth rate is 0.1493 (approx) or 14.93% (approx)

c) in the 4th week   the weekly number of specialty items produced at the new factory exceed the weekly number of specialty items produced at the old factory.

step-by-step explanation:

according to question,

the function that shows the total number of the product in w week by the old factory is,

let the function that shows the total number of product in w week by new factory,

with of regression formula, a = 190.9139081≈190.914

and,   b = 1.149328018≈1.1493

thus, the function that shows the total number of product in w week by new factory,

where 1.1493 is growth factor and 0.1493 is the growth rate of the function p'(w).

a) if x=0

from the given graph, p'(0) = 190 (approx)

since, p(0)-p'(0)=230-190=40

thus,   40 more specialty items were produced at the old factory than at the new factory.

b) growth rate for p(x) is 0.10 and for p'(x) is 1.149 (apprx)

since, 1.149> 0.10

thus, the growth rate of the weekly number of specialty item by new factory is more the that of old factory.

c) at x = 4

p'(4) = 337 ( by the given graph)

since, p'(4)> p(4)

thus, at 4th week the weekly number of specialty items produced at the new factory exceed the weekly number of specialty items produced at the old factory.