a$.$ Obtain the linear trend equation for the following data on new checking accounts at Fair Savings Bank and use it to predict expected new checking accounts for periods $16$ through $19.($Round your intermediate calculations and final answers to $2$ decimal places.$)$

Period New Accounts Period New Accounts Period New Accounts

$1200623211281$

$2214724812275$

$3211825013280$

$4228925314288$

$52351026715310$

b$.$ Use trend$-$adjusted smoothing with $\backslash$alpha $=0\mathrm{.}3$ and $\backslash$beta $=0\mathrm{.}2$ to smooth the new account data in part a$.$ What is the forecast for period $16?$ Compute the initial trend estimate $($Tt$)$ for Period $5$ as follows: $($Period $4$ data $$ Period $1$ data$)/3.$ Then compute the initial trend$-$adjusted forecast $($TAFt$)$ for Period $5$ as follows: Period $4$ data $+$ Initial trend estimate for Period $5.$ Then compute all remaining values $($including the St value for Period $5)$ using the textbook formulas or Excel template. $($Round the "Trend" values to $3$ decimal places and other values to $2$ decimal places for intermediate calculations. Round your final answer to $2$ decimal places.$)$