To find the starting temperature of the tea when it was first set out to cool, we need to determine the temperature at time [tex]\( t = 0 \)[/tex] minutes. The equation given to represent the cooling process is:
[tex]\[ f(t) = 109(0.935)^t + 72 \][/tex]
Here, [tex]\( t \)[/tex] denotes the number of minutes that have passed since the tea started cooling.
To find the starting temperature, substitute [tex]\( t = 0 \)[/tex] into the equation:
[tex]\[ f(0) = 109(0.935)^0 + 72 \][/tex]
Any number raised to the power of 0 is 1:
[tex]\[ (0.935)^0 = 1 \][/tex]
So, the equation simplifies to:
[tex]\[ f(0) = 109 \cdot 1 + 72 \][/tex]
[tex]\[ f(0) = 109 + 72 \][/tex]
[tex]\[ f(0) = 181 \][/tex]
Thus, the starting temperature of the tea, when time [tex]\( t \)[/tex] was 0, is [tex]\( 181^\circ \)[/tex] Fahrenheit.
Therefore, the correct answer is:
[tex]\[ 181^\circ \][/tex]
