Look at pic The function f(x)=223(1.09)^x represents the number of specialty items produced at Iron Man’s old factory x weeks after a change in management. The graph represents the number of specialty items produced at the new factory during the same time period.

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

a. 33

b. So we see that at the start of 3rd week, the new factory begins to exceed old production.

Step-by-step explanation:

(a)w = 0

Old factory: p(x)=223(1.09)^x Plug in 0

p(0)= 223(1.09)^(0)

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

p(0) = 223(1)

p(0) = 223

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

223 - 190 = 33

During Week 0, 33 more specialty items were produced at the old factory than at the new factory.

(b) i don't know sorry

(c)

The old production tabulated:

w P(w) New

0 223 190

1 243 220

2 265 252

3 289 290

4 315 337

5 343 380

6 374 440

7 408 505

So we see that at the start of 3rd week, the new factory begins to exceed old production.

i hope this helped people in the future.