Pls check my work.....
Hi, anyone care to check and see if I got this right?
A sociologist is studying the crime rate in a certain town. She uses a model which estimates that t months after the beginning of next year the number of crimes will increase at a rate given by t + sin(t) crimes per month.
i) Estimate the total number of crimes that can be expected to be committed next year.
ii) How many crimes can be committed in the last 6 months of next year?
ii)(12+cos(12)) - (5+cos(5))=7.56
The rate increases per 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.