Question

If current trends continue, future concentration of atmospheric CO2 in parts per million could reach levels shown in the table. The CO2 concentration in the yr 2000 was greater than it had been in the previous 160,000 yrs.
yr 2000 2050 2100 2150 2200

CO2 364 467 600 769 987
ppm

find values for C and a so that f(x) = Ca* models the data.

graph f and the data in the same viewing rectangle

Answer 1

i would start counting at year 2000 and make that 0, so that C = 364 the initial value. i would also use x and 50y where y was the number of years. then

put \[364a=467\] and solve for a
get
\[x=\frac{467}{364}=1.28\] rounded meaning a 28% increase every 50 year. formula would be
\[364(1.28)^x\]

Answer 2

where x is in units of 50 year. we can check to see if it is good.

Answer 3

\[364(1.28)^2=596.37\] pretty close

Answer 4

of course x = 2 means 100 years. we can check the next one as well.
\[364(1.28)^3=763.36\] also close

Answer 5

if
\[a=1.28\] is too small it is because i rounded
\[\frac{467}{364}\]

Answer 6

take more digits might be more accurate, but it is just a model yes?

Answer 7

\[364(1.28)^4=977\] so maybe want more decimal accuracy. if you want the exponent to be in years rather than in units of 50 years just write
\[364(1.28)^{\frac{x}{50}}\]