hello can someone please help me with these calculus questions please and thank you Problem $\backslash$#$5$: A hot drink is taken outside on a cold winter day when the air temperature is $\backslash (-8^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ According to a principle of physics called Newton's Law of Cooling, the temperature $\backslash ($ T $\backslash )($in degrees Celsius$)$ of the drink $\backslash ($ t $\backslash )$ minutes after being taken outside is given by

$\backslash [$

T$($t$)=-8+$A e$^\{-$k t$\}$

$\backslash ]$

where $\backslash ($ A $\backslash )$ and $\backslash ($ k $\backslash )$ are constants.

$($a$)$ Suppose that the temperature of the drink is $\backslash (87^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ when it is taken outside. Find the value of the constant $\backslash ($ A $\backslash ).$

$($b$)$ In addition, suppose that $20$ minutes later the drink is $\backslash (29^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Find the value of the constant $\backslash ($ k $\backslash ).$

$($c$)$ What will the temperature be after $29$ minutes?

$($d$)$ When $($i$.$e$.,$ after how many minutes$)$ will the temperature reach $\backslash (0^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )?$

Problem $\backslash$#$5($a$)$:

Problem $\backslash$#$5($b$)$:

Round your answer to $6$ decimals.

Problem $\backslash$#$5($c$)$:

Round your answer to $2$ decimals.

Problem $\backslash$#$5($d$)$:

Round your answer to $2$ decimals.

Submit Problem $\backslash$#$5$ for Grading