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CCSS.Math: , , , , , ,

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 let me highlight that because that's not a typical unit but in decades since co2 levels were first measured and the total amount of co2 in the atmosphere so the amount of co2 a of Dec sub decade of T in parts per million is modeled by the following function so the amount of co2 as a function of how many decades have passed is going to be this so T is in decades in this in this model right over here complete the following sentence about the yearly rate of change the yearly rate of change and the amount of co2 in the atmosphere round your answer two decimal places every year the amount of co2 in the atmosphere increases by a factor of if they said every decade well this would be pretty straightforward every decade you increase T by one and so we're going to multiply by 1.06 again so every decade you increase by a factor of 1.06 but what about every year and I always find it helpful to make a bit of a table so we can really digest things properly so I'll say T and I'll say a of T so when T is equal to zero so at the beginning of our study well 1.06 to the zero power shouldn't be one you have three hundred and fifteen parts per million so what's a year later so a year later is going to be 1/10 of a decade remember T is in decades so a year later is 0.1 of a decade so 0.1 of a decade later what is what is going to be the amount of carbon we have well it's going to be 315 times 1.06 to the to the 0.1 power and what is that going to be well let's see if we so one 0.06 to the so to the zero zero point one power I didn't have to do actually use of parentheses there is equal to one point zero zero five eight I'll just take it with that it's one point zero zero five eight so this is the same thing it's three point five times one point zero zero five eight and I should say approximately equal to I did a little bit of rounding there so after another year so now we're at T equals zero point two or at two tenths of a decade where we're gonna be we're going to be at three point five times one point oh six to the zero point two which is the same thing as three point five times one point zero six to the zero point one and then that raised to the second power so we're going to multiply by this one point zero six to the tenth to the one tenth power again we're gonna multiply by one point zero zero five eight a second time another way to think about if we want to reformulate this model in terms of years so per year of T it's going to be three hundred and fifteen and now our common ratio wouldn't be 1.06 it would be 1.06 to the point one power or one point zero zero five eight and then we would raise that now T would be in years now here it is in decades and I could say approximately since this is rounded a little bit and so every year the amount of co2 in the atmosphere increases by a factor of I could say 1.06 to the zero point one power but if I'm if I'm rounding my answer to two decimal places the well we're gonna increase by one point zero zero five eight in fact they should they increases by a factor of they should I I'm guessing they want more than two deaths two decimal places well anyway this this is arguably this is this right over here is five significant digits I'll leave it there