A valve on a storage tank is opened for $4$ hours to release a chemical in a manufacturing process. The flow rate $R($in liters per hours$)$ at a time $t($in hours$)$ is given in the table.

$\backslash$table$[[t,0,1,2,3,4],[R,423,238,118,69,34]]$

$($a$)$ Use the linear regression capabilities of a graphing utility to find a linear model for the points $(t,ln(R)).$ Write the resulting equation of the form $ln(R)=at+b$ in exponential form. $($Round your coefficients to four decimal places.$)$

$R=$

$($b$)$ Use a graphing utility to plot the data and graph the exponential model. $($Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.$)$

$$

$($c$)$ Use the definite integral to approximate the number of liters of chemical released during the $4$ hours. $($Round your answer to one decimal place.$)$

${\displaystyle \underset{0}{\overset{4}{}}}R(t)dt=,L$