The amount of carbon dioxide (CO2) in the atmosphere increases rapidly as we continue to rely on fossil fuels.The relationship between the elapsed time, t, in decades, since CO2 levels were first measured, and the total amount of CO2 in the atmosphere, Adecade (t), in parts per million, is modeled by the following function:Adecade (t)=315⋅(1.06)tComplete the following sentence about the yearly rate of change in the amount of CO2 in the atmosphere.Round your answer to four decimal places.Every year, the amount of CO2 in the atmosphere increases by a factor of
Q. The amount of carbon dioxide (CO2) in the atmosphere increases rapidly as we continue to rely on fossil fuels.The relationship between the elapsed time, t, in decades, since CO2 levels were first measured, and the total amount of CO2 in the atmosphere, Adecade (t), in parts per million, is modeled by the following function:Adecade (t)=315⋅(1.06)tComplete the following sentence about the yearly rate of change in the amount of CO2 in the atmosphere.Round your answer to four decimal places.Every year, the amount of CO2 in the atmosphere increases by a factor of
Understand function representation: Understand the given function and what it represents.The function Adecade(t)=315×(1.06)t models the total amount of CO2 in the atmosphere in parts per million as a function of time in decades since CO2 levels were first measured. The base amount of CO2 is 315ppm, and it increases by a factor of 1.06 every decade.
Determine yearly rate change: Determine the yearly rate of change.Since the function gives the amount of CO2 after t decades, we need to find the equivalent yearly rate of change. There are 10 years in a decade, so we need to take the 10th root of 1.06 to find the yearly rate of change.
Calculate 10th root: Calculate the 10th root of 1.06. The 10th root of 1.06 can be calculated using the formula (1.06)101.
Perform calculation: Perform the calculation.Using a calculator, we find that (1.06)101 is approximately equal to 1.0058 when rounded to four decimal places.
Interpret yearly increase: Interpret the result.The calculation shows that every year, the amount of CO extsubscript{2} in the atmosphere increases by a factor of approximately 1.0058.
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