If current rates of deforestation and fossil fuel consumption continue, then the amount of atmospheric carbon dioxide in parts per million (ppm) will be given by f(x)=375e^0.00609c, where c=0 corresponds to 2000.
a)What is the amount of carbon dioxide in 2022?
b)In what year will the amount of carbon dioxide reach 500ppm?
To determine the amount of carbon dioxide in 2022 using the given function, we need to find the value of f(x) when x represents the year.
a) To find the amount of carbon dioxide in 2022, we substitute x = 2022 into the function f(x) = 375e^0.00609c, where c = 0 corresponds to the year 2000.
f(2022) = 375e^0.00609(2022-2000)
f(2022) = 375e^0.00609(22)
f(2022) ≈ 375e^0.134
f(2022) ≈ 375(1.144)
f(2022) ≈ 429 ppm
Therefore, the amount of atmospheric carbon dioxide in 2022 is estimated to be approximately 429 parts per million (ppm).
b) To find the year when the amount of carbon dioxide reaches 500ppm, we need to solve the equation f(x) = 500.
500 = 375e^0.00609c
Dividing both sides of the equation by 375, we get:
e^0.00609c = 500/375
e^0.00609c ≈ 1.333
To isolate the exponent, we take the natural logarithm (ln) of both sides:
ln(e^0.00609c) = ln(1.333)
0.00609c = ln(1.333)
Dividing both sides of the equation by 0.00609, we find:
c ≈ ln(1.333) / 0.00609
c ≈ 69.19
Since c represents the number of years past 2000, we can then find the year:
Year = 2000 + c
Year ≈ 2000 + 69.19
Year ≈ 2069
Therefore, the amount of carbon dioxide is estimated to reach 500 ppm in the year 2069.