Problem 121 - College Algebra Essentials

Question

There are approximately \(3.2 \times 10^{7}\) seconds in a year. According to the United States Department of Agriculture, Americans consume 127 chickens per second. How many chickens are eaten per year in the United States? Express the answer in scientific notation.

Step-by-Step Solution

Answer

The number of chickens that are eaten per year is approximately \(4.064 \times 10^{9}\)

Step 1: Convert Chicken Consumption Rate From Per Second To Per Year

Firstly, determine how many chickens are eaten in a year. Given that Americans consume 127 chickens per second, multiply this by the amount of seconds in a year (approximately \(3.2 \times 10^{7}\)) to convert the rate to per year, i.e., \(127 \times 3.2 \times 10^{7}\).

Step 2: Calculate The Number Of Chickens Consumed Per Year

The above multiplication gives \(406.4 \times 10^{7}\) chickens as the number of chickens consumed per year.

Step 3: Express The Answer In Scientific Notation

Finally, the answer needs to be in scientific notation. To put the number \(406.4 \times 10^{7}\) into correct scientific notation, we must adjust the number so that it is between 1 and 10, then adjust the power of ten so the value stays the same. This gives \(4.064 \times 10^{9}\).