The rateincreasesper month, so the number of crimes are not constant per month.

(i) The number of crimes in the first year is the sum from 1 to 12 of t + sin(t)

= (1 + sin(1)) + (2 + sin(2)) + ... +(12 + sin(12))

= (1 + 2 + ... + 12) + (sin(1) + sin(2) + ... + sin(12))

= 78 + the sum from 1 to 12 sin(t)

(ii) use sigma sums to express the number of crimes in 24 months, then in 20 months, and then subtract number of crimes in the 20 months from the 24 since month 0.