Select the correct answer. Henry is
O an economist and wants to understand the relationship between inflation and consumer spending habits. For his
research, he
needs the Consumer Price Index for 2014 and the inflation rate. Based on the
prices of goods given, what will he find to
be the CPI and
inflation rate
for 2014? Assume that a consumer's basket for three consecutive years consists of the following:
Year
Price of an Apple
Number of Apples
Consumed
Price of an Orange
Number of Oranges
Consumed
2012
2
3
3
2013
3
2
2014
5
5
Consider 2012 to be the base year.
O A.
100 CPI, 49.56 percent inflation
• B.
165 CPI, 45.40 percent inflation
O C.
185 CPI, 55.35 percent inflation
O D.
175 CPI, 60.56 percent inflation
O E.
125 CPI, 50.60 percent inflation

you forgot an image

step-by-step explanation:

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.