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Hot tea is cooling in a room that has a temperature of [tex]72^{\circ}[/tex] Fahrenheit. The equation that represents this model is [tex]f(x) = 109(0.935)^t + 72[/tex], where [tex]t[/tex] represents the number of minutes that pass. What was the starting temperature of the tea?

A. [tex]174^{\circ}[/tex]
B. [tex]72^{\circ}[/tex]
C. [tex]109^{\circ}[/tex]
D. [tex]181^{\circ}[/tex]

Sagot :

GinnyAnswer
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]
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