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 specalty items produced at the new factory during the same time period. ( Answer A, B,C Explain and Show you work): A) During Week O, how many more specialty items were produced at tbe 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. [ Look at the picture for the graph]. Will Mark Brainliest.

A) 20 items more

              B) Growth rate for old factory: r = 0.1

                   Growth rate for new factory: r = 0.15

              C) After 4 weeks

Step-by-step explanation: A) The function p(w) is a growth exponential function. To determine the difference, substitute w=0 for the old factory

p(0) = 230

According to the graph, for the new factory, at week 0, it was produced:

p(0) = 190

Then, the difference is

230 - 190 = 20

Old factory produced 20 items more than the new factory during week 0.

B) Exponential functions are of the form: where:

a is initial value

r is percent growth rate

For old factory, growth rate is

1 + r = 1.1

r = 0.1

For new factory:

r = 0.15

The new factory has a growth rate of 15% compare to the old factory, whose rate is 10%.

C) At week 0, we already know old produces more than new. However, as growth rate of new is higher than the old, at some moment, both will be approximately the same and then, new will exceed old. So, to determine when this happens, find when they are the same.

To compare them, we have to express the new factory exponential function:

Now:

w = 4.33

At week 4, both factories will produce approximately the same amount of items. From week 5, new factory will be producing more than old factory. So, at week 5, the weekly number of specialty items produces at the new factory will exceed the old factory.

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step-by-step explanation: