Question 1197444
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Part (a)


t is the number of years since 1750
t = 0 represents 1750
t = 1 represents 1751
and so on


The year 1975 means t = 1975-1750 = 225
The gap from 1750 to 1975 is 225 years
Use this idea for the other years of 2000, 2050, and 2100.


Use spreadsheet software to quickly compute the outputs.
You'll need to type in the <font color=blue>exp</font> function instead of something like e^x
Example calculation:  <font color=blue>=280*EXP(0.00127*225)</font>  yields the approximate result of 372.612722644863 which rounds to 373.


This is what you should get when rounding each C(t) value to the nearest whole number.
<table border = "1" cellpadding = "5"><tr><td>Year</td><td>t = Number of years since 1750</td><td>C(t) = Amount of CO2 (ppm)</td></tr><tr><td>1975</td><td>225</td><td>373</td></tr><tr><td>2000</td><td>250</td><td>385</td></tr><tr><td>2050</td><td>300</td><td>410</td></tr><tr><td>2100</td><td>350</td><td>437</td></tr></table>ppm = parts per million


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Part (b)


The table above shows 
C(225) = 373 .... year 1975
C(250) = 385 .... year 2000


The level surpasses 380 ppm between the years 1975 and 2000.
It's likely it's somewhere close to the year 2000 compared to the year 1975.


Use a natural logarithm to determine a more accurate time value.
C(t) = 280*e^(0.00127t)
380 = 280*e^(0.00127t)
380/280 = e^(0.00127t)
0.00127t = Ln(380/280)
t = Ln(380/280)/0.00127
t = 240.457991772584


Rounding to the nearest year gets us t = 240
240 years after 1750 is 1750+240 = 1990 which also is the start of a decade, meaning we don't have to round to the nearest decade.


Answer: <font color=red>1990</font> 
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