Suppose x grows at a rate
Percent and y grows at a rate
Percent.If z = y · x,then z grows at __________;while if z = x/y,z grows at __________.
A)7 percent;-17 percent
B)-17 percent;7 percent
C)17 percent;-7 percent
D)60 percent;42 percent
E)60 percent;-42 percent

Question

Suppose x grows at a rate 
Percent and y grows at a rate 
Percent.If z = y · x,then z grows at __________;while if z = x/y,z grows at __________.
A)7 percent;-17 percent 
B)-17 percent;7 percent 
C)17 percent;-7 percent 
D)60 percent;42 percent 
E)60 percent;-42 percent

Quizplus · Accepted Answer

If z = y · x, then its growth rate can be found by adding the growth rates of x and y:

z' = (1 + 11ea895d_4d3b_ccfa_8397_37b425571793_TB4305_11) * (1 + 11ea895d_4d3b_ccfb_8397_7568d0999e56_TB4305_11) - 1

= 1.11 * 1.11 - 1

= 0.2321 or 23.21%

So z grows at 23.21%

If z = x/y, then we can find its growth rate using the formula for division:

z' = [(1 + 11ea895d_4d3b_ccfa_8397_37b425571793_TB4305_11) / (1 + 11ea895d_4d3b_ccfb_8397_7568d0999e56_TB4305_11)] - 1

= [1.11 / 0.89] - 1

= 0.2472 or 24.72% (rounded)

So z grows at 24.72%

Therefore, the answer is C, 17 percent;-7 percent.

Suppose X Grows at a Rate