Let's break down the problem step by step: **Problem Restatement:** A person releases CO₂ via respiration at a rate of 0.97 mg/s. How long (in years) would it take for that person to release 4.60 metric tons of CO₂ (the amount a typical passenger vehicle releases annually)? Note: 1 metric ton = 1000 kg. --- ### **Step 1: Convert the Target Mass to Milligrams** **Given:** - Target CO₂ mass = 4.60 metric tons - 1 metric ton = 1000 kg - 1 kg = 1,000,000 mg **Calculation:** 4.60 metric tons × 1000 kg/metric ton × 1,000,000 mg/kg = 4.60 × 1000 × 1,000,000 mg = 4,600 × 1,000,000 mg = **4,600,000,000 mg** --- ### **Step 2: Calculate Time Required in Seconds** **Given:** - Rate of CO₂ release = 0.97 mg/s - Total mass to be released = 4,600,000,000 mg **Calculation:** Time (in seconds) = (Total mass) / (Rate) = 4,600,000,000 mg / 0.97 mg/s ≈ **4,742,268,041 s** --- ### **Step 3: Convert Time from Seconds to Years** **Given:** - 1 year = 365.25 days × 24 hours × 60 minutes × 60 seconds = 31,557,600 seconds **Calculation:** Time (in years) = 4,742,268,041 s / 31,557,600 s/year ≈ **150.4 years** --- ## **Final Answer:** It would take approximately **150 years** for a person to release 4.60 metric tons of CO₂ via respiration at an average rate of 0.97 mg/s.

The concept involves unit conversion and proportional reasoning. First, convert the target amount of CO₂ from metric tons to milligrams to match the units of the release rate. Then, divide the total mass by the rate of release to find the total time in seconds. Finally, convert this time from seconds to years using the standard number of seconds in a year. This process applies fundamental principles of unit conversion and simple division to determine the duration required for a cumulative amount to be released at a constant rate.

The problem is about figuring out how long it takes for a person to breathe out a certain amount of carbon dioxide. First, we need to change the total amount of CO₂ from metric tons into milligrams because the breathing rate is given in milligrams per second. This involves converting tons to kilograms, then kilograms to milligrams. Next, we divide the total amount in milligrams by the rate at which CO₂ is released (0.97 mg/sec) to find out how many seconds it would take. Lastly, we convert those seconds into years by dividing by the number of seconds in a year. So, by doing these conversions and calculations step-by-step, we find that it would take about 150 years for a person to release 4.60 metric tons of CO₂ at that rate.

Certainly! Here's an explanation of the reasoning process in simple language: The problem asks how long it would take for a person to exhale a total amount of CO₂ equivalent to 4.60 metric tons, given that they breathe out CO₂ at a rate of 0.97 milligrams per second. To solve this, we first need all measurements in compatible units. Since the total amount is given in metric tons, we convert it into milligrams because our rate is in milligrams per second. We do this by first changing metric tons to kilograms (multiplying by 1000) and then kilograms to milligrams (multiplying by 1,000,000). Once we have the total CO₂ in milligrams, we divide that by the rate (0.97 mg/sec) to find out how many seconds it would take. Finally, because seconds are a very small unit, we convert the total seconds into years by dividing by the number of seconds in a year (about 31.5 million). This step-by-step approach helps us understand how long it would take, and the final answer is roughly 150 years.