Question

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.​

Answer 1

Answer:

40 more specialty items were produced at the old factory than at the new factory. p(w)=230(1.1)^w. w=0. Old factory=230. New factory=190. 230-190=40.  

B.

f(x)=a(1+r) ^x. a= initial value. r=percent growth rate.  

p(w)=230(1.1)^w=growth rate for the old factory.  1+r=1.1. r=0.1.  

220=190(1+r) ^1= growth rate for the new factory. 1+r=220/190. 1+r=1.15. r=0.15.  

Therefore, while the new factory’s growth rate is 0.15=15%, the old factory’s growth rate is 0.1=10%. Thus, the production of the new factory is growing faster.  

C. The week the new factory started producing more specialty items than the old factory is on the 4th week.

Week 1 2 3 4 5 6 7

Old Factory 253 278.3 306.13 336.743 370.417 407.459 448.205

New Factory 220 252 290 337 380 440 505

Difference -33 -26.3 -16.13 0.257 9.583 32.541 56.795

 

Step-by-step explanation: