Problem 146 - College Algebra Essentials

Question

Our hearts beat approximately 70 times per minute. Express in scientific notation how many times the heart beats over a lifetime of 80 years. Round the decimal factor in your scientific notation answer to two decimal places.

Step-by-Step Solution

Answer

The heart beats approximately \(2.94 \times 10^{9}\) times over a lifetime of 80 years.

Step 1: Calculate the total beats per minute in a year

Firstly, calculate the total number of minutes per year by multiplying the minutes per hour, hours per day, and days per year (60 minutes times 24 hours times 365.25 days). Then, multiply this result by the number of heart beats per minute. So it's \( 70 \ times 60 \ times 24 \ times 365.25 \). Calculate this expression to get the total heartbeats in a year.

Step 2: Calculate the total beats in 80 years

Secondly, find out the total number of heartbeats in a lifetime of 80 years. Multiply the number of heartbeats in a year by 80. That would be the result from Step 1 times 80.

Step 3: Convert the total beats to scientific notation

Next, convert this final number to scientific notation. Remember, a number in scientific notation is expressed as \(a \times 10^n \), where \(1 \leq a < 10 \) and \(n \) is an integer. Adjust the decimal point of the number to obtain a factor \(a \) that is between 1 and 10, noting the positions moved as the exponent \(n\). If the decimal was moved to the left, \(n \) is positive; if to the right, \(n \) is negative. Also, it's necessary to round the decimal factor (\(a\)) to two decimal places.