Question

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.

Answer 1

Answer:

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.

Answer 2

During week 0 the old factory produced 33 more items than at the new factory.

The weekly number of specialty items produced at the new factory exceed the weekly number of specialty items produced at the old factory at week 4.

What is a function?

A function is defined as a relation between a set of inputs having one output each. A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain or range.

According to the given problem,

Specialty items produced at the old factory at week 0,

Given function = $223(1.09)^{x}$

When x = 0,

f(x) = $223(1.09)^{0}$

     = 223

Specialty items produced at the new factory during 0 = 190

Old factory exceeded the production by:

⇒ ( 223 -  190 )

= 33 specialty items.

Comparing the growth rates of weekly number of specialty items at each factory,

For week 0,

Old factory = 223

New factory = 190

Growth rate = $\frac{223-190}{190}*100$

                    ≈ 17%

For week 1,

Old factory = 243

New factory = 220

Growth rate = $\frac{243.07-220}{220}*100$

                    ≈ 10%

For week 2,

Old factory = 265

New factory = 252

Growth rate = $\frac{264.95-252}{252}*100$

                    ≈ 5%

For week 3,

Old factory = 289

New factory = 290

Growth rate = $\frac{290 -288.79}{288,79}*100$

                    ≈ 0.41%

For week 4,

Old factory = 325

New factory = 337

Growth rate = $\frac{337-324.78}{324.78}*100$

                    ≈ 3%

For week 5,

Old factory = 343

New factory = 380

Growth rate = $\frac{380-343.11}{343.11} *100$

                    ≈ 13%

For week 6,

Old factory = 374

New factory = 440

Growth rate = $\frac{440-374}{374} *100$

                    ≈ 18%

For week 7,

Old factory = 408

New factory = 505

Growth rate = $\frac{505-408}{408} *100$

                   ≈ 23%

At week 3, the production at new factory exceeds the production of the old factory.

For old factory,

⇒ f(x) = $223(1.09)^{x}$

          = $223(1.09)^{3}$

          = 289

For new factory at week 3,

Production = 290 items.

Hence, we can conclude, during week 0 the old factory produced 33 more items than at the new factory and the weekly number of specialty items produced at the new factory exceed the weekly number of specialty items produced at the old factory at week 4.

Learn more about functions here: https://brainly.com/question/12431044

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