Answer:
Step-by-step explanation:
a. during week 0, the old factory produced p(w)=230(1.1)^0 specialty items.
anything to the 0th power is 1 so 230(1) = 230 specialty items.
the new factory, as shown on the graph, produced 190 specialty items on week 0.
to find how many more were produced at the old factory, do 230 - 190 to get 40 specialty items.
b. the growth rate is given for the old factory p(w)=230(1.1)^0
to find the growth rate of the new factory, you need to plug in points.
we know that at w = 0, f(w) is 190.
p(w) =
to find the value of ? , plug in values for w and p(w).
220 =
220 =
the rate is 22/19
check this by doing it again.
252 =
252/190 = ? ^2
the square root of 252/190 is 22/19, so ? is 22/19.
therefore the equation is p(w) = 190(22/19)^w
when comparing the growth rates, the new factory produces more items in less time.
c. in order to find when the produced items at the new factory exceeds the old factory, we need to graph the old factory's function.
once graphed, it is found that at w=5 the new factory exceeds the weekly number of specialty items produced at the old factory.
the old factory's function is p(w)=230(1.1)^w
at w = 5, p(w)=230(1.1)^5 = 230(1.61051) = 370.4
380 is greater than 370.4 so week 5 is the answer.
