Help me solve this problem with thoroughly shown work. Then, give me $8$ reasons and with backed up math evidence as to why your answer is correct and show me the correlating step to your evidence. A mathematician will be presented this, so make it as accurate as possible. Tutoring Center needs to allocate tutors this week for office appointments, so it needs to forecast the number of students who will seek appointments. The director has gathered the following time series data recently:

Period Student Appointments

$4$ weeks ago $100$

$3$ weeks ago $90$

$2$ weeks ago $80$

Last week $70$

What would naive forecasting suggest as the number of student appointments that can be expected this week?

What is this week$$s forecast for student appointments using a $3-$weeks simple moving average? What would the same forecast be using a $3-$weeks weighted moving average with the following weights: $0\mathrm{.}50,0\mathrm{.}35,$ and $0\mathrm{.}15?$

What would be this week$$s forecast for student appointments using exponential smoothing with alpha of $0\mathrm{.}25,$ if the forecast for $2$ weeks ago was $90?$

The answer should be given in the following format: Naive Forecasting Value; $3-$weeks simple moving average value; $3-$weeks weighted moving average value; Exponential smoothing forecasting value.

Question $11$ options:

$70$; $80$; $76\mathrm{.}5$; $87\mathrm{.}5$

$70$; $80$; $76\mathrm{.}5$; $86\mathrm{.}875$

$70$; $80$; $76\mathrm{.}5$; $83\mathrm{.}125$