# no. of minutes requiredtoprocessthe kth regs. is about f(k) = 6(1 + k)-1/3. Find definite integral to est.time for one person to keyboard 600 regs. A data processor keyboards registration data for college students from written forms to electronic files. The number of minutes required to process the kth registration is estimated to be approximately f(k) = 6(1 + k)-1/3. Use a definite integral to estimate the time required for one person to keyboard 600 registrations. The number of minutes required to process the kth reg is f(k),

`f(k) = 6(1+k)^(-1/3)` (I am assuming this is teh function, beacuse it is not clear, if it is `f(k) = 6(1+k)-1/3`  then you can follow this for it.

if you draw a graph of f(k) against k, then the area under that curve will give the time required to process all the regs, in other words, you have tp integrate,

therefore the total time required is, T

`T = intf(k)dk`

the time required to process 600 regs,

`T = int_0^600(6(1+k)^(-1/3))dk`

`int(6(1+k)^(-1/3))dk = (6(1+k)^((-1)/3+1))/((-1)/3+1)`

`= 9(1+k)^(2/3)`

therefore the total time required, T is,

`T = 9((1+600)^(2/3)-1) = 631.95`

the total time required to process 600 units is 631.95 minutes.

Approved by eNotes Editorial Team