Question

Between 1852 and 2005​, carbon dioxide (CO2​) concentration in the atmosphere rose from roughly 290 parts per million to 377 parts per million. Assume that this growth can be modeled with an exponential function: Upper Q equals Upper Q 0 times left parenthesis 1 plus r right parenthesis Superscript tQ=Q0×(1+r)t.

a. By experimenting with various values of the growth rate​ r, find an exponential function that fits the data for 1852 and 2005.

r ≈

​(Round to five decimal places as​ needed.)

b. Use this exponential model to predict when the CO2 concentration will double its1852 level. According to this​ model, the CO2 concentration will double its 1852

level in...

​(Type a whole​ number.)

Answer 1

Between 1852 and 2005, carbon dioxide (CO2) concentration in the atmosphere rose from roughly 290 parts per million to 377 parts per million. Assume that this growth can be modeled with an exponential function: Upper Q equals Upper Q 0 times left parenthesis 1 plus r right parenthesis Superscript tQ=Q0×(1+r)t.

a)

whare Q0 represent the CO2 concentration in the at mosphere in  1852.

and Qt represent the CO2 concentration in the atmosphere after t years of  1852

Q0 = 290 parts per million ( in  1852 )

Q128 = 377 parts per million ( in 2005 ofter 128 year of 1852 )

= 377 = 290 ( 1+ r )153

= 377 / 290 = ( 1+ r ) 153

= 1 + r = (   377 / 290 ) 1/153

= 1 + r = 1.00171

r = 0.00171

Hence Qt = Q 0 ( 1+0. 00171)t

Concentration of CO2 in 2005 = 290 ( 1 +  0.00171)153

b)

Suppose CO2 concentraion double in t years of  1852 level. 2 290 = 580 parts / million

580 = 290 ( 1 + 0.00171 ) t

= ( 1+ 0.00171 )t =2

= ( 1.00171 ) t = 2

= t log ( 1.00171 ) = log 2

= t = log ( 2 ) / log ( 1. 00171 ) = 0.301029 / 0.000742 =405

CO2 concentreation will double 1852 level ofter405 years ( i.e in 1852 + 405 ) = 2257