An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Calculate the Consumer Price Index (CPI) for year XXX1: CP I XXX 1 = 3740 .
Calculate the Consumer Price Index (CPI) for year XXX2: CP I XXX 2 = 3970 .
Calculate the inflation rate using the formula: I n f l a t i o n R a t e = CP I XXX 1 CP I XXX 2 − CP I XXX 1 × 100 .
The inflation rate from year XXX1 to year XXX2 is approximately 6.15% .
Explanation
Understanding the Problem We are given the Consumer Price Index (CPI) for two years, XXX1 and XXX2, across various categories. Our goal is to calculate the inflation rate between these two years using the CPI data.
Calculating CPI for Year XXX1 First, we need to calculate the CPI for year XXX1 by summing the values for each category:
CP I XXX 1 = Ho u s in g XXX 1 + F oo d XXX 1 + T r an s p or t a t i o n XXX 1 + M e d i c a l XXX 1 + E d u c a t i o n XXX 1 + A pp a re l XXX 1 + R ecre a t i o n XXX 1 + Ot h e r XXX 1
Summing the Values for Year XXX1 Plugging in the values from the table:
CP I XXX 1 = 1410 + 420 + 280 + 400 + 560 + 210 + 120 + 340 = 3740
Calculating CPI for Year XXX2 Next, we calculate the CPI for year XXX2 by summing the values for each category:
CP I XXX 2 = Ho u s in g XXX 2 + F oo d XXX 2 + T r an s p or t a t i o n XXX 2 + M e d i c a l XXX 2 + E d u c a t i o n XXX 2 + A pp a re l XXX 2 + R ecre a t i o n XXX 2 + Ot h e r XXX 2
Summing the Values for Year XXX2 Plugging in the values from the table:
CP I XXX 2 = 1460 + 430 + 310 + 500 + 610 + 200 + 140 + 320 = 3970
Calculating the Inflation Rate Now, we calculate the inflation rate using the formula:
I n f l a t i o n R a t e = CP I XXX 1 CP I XXX 2 − CP I XXX 1 × 100
Substituting the CPI Values Substituting the calculated CPI values:
I n f l a t i o n R a t e = 3740 3970 − 3740 × 100 = 3740 230 × 100 ≈ 6.149732620320856
Final Answer Therefore, the inflation rate from year XXX1 to year XXX2 is approximately 6.15%.
Examples
Understanding inflation rates is crucial for making informed financial decisions. For instance, if you're considering investing in a bond with a 5% return, but the inflation rate is 6.15%, your real return (accounting for inflation) is negative. This means your purchasing power actually decreases over time. By calculating and understanding inflation, you can better assess the true value of investments, salary increases, and the cost of goods and services.
To determine how many electrons flow through an electric device that delivers a current of 15.0 A for 30 seconds, we first calculate the total charge, which is 450 C. We then divide this charge by the charge of a single electron (approximately 1.6 x 10^-19 C), resulting in approximately 2.81 x 10^21 electrons. Thus, about 2.81 x 10^21 electrons flow through the device in 30 seconds.
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