Kao measured the temperature of a cup of hot chocolate placed in a room with a constant temperature of 70

Question

Kao measured the temperature of a cup of hot chocolate placed in a room with a constant temperature of 70 degrees Fahrenheit (°F). The temperature of the hot chocolate was 185°F at 6:00 p.m. when it started cooling. The temperature of the hot chocolate was 156°F at 6:05 p.m. and 135°F at 6:10 p.m. The hot chocolate’s temperature continued to decrease. Of the following functions, which best models the temperature $T of m$ , in degrees Fahrenheit, of Kao’s hot chocolate m minutes after it started cooling?

A.

$T of m equals, 185 times, 1 point 2 5 to the m power$

B.

$T of m equals, 185 times, 0 point 8 5 to the m power$

C.

$T of m equals, open parenthesis, 185 minus 70, close parenthesis, times, 0 point 7 5 raised to the m over 5 power$

D.

$T of m equals, 70 plus, 115 times, 0 point 7 5 raised to the m over 5 power$

Accepted Answer

Choice D is correct. The hot chocolate cools from 185&deg;F over time, never going lower than the room temperature, 70&deg;F. Since the base of the exponent in this function, 0.75, is less than 1, decreases as time increases. Using the function, the temperature, in &deg;F, at 6:00 p.m. can be estimated as and is equal to . The temperature, in &deg;F, at 6:05 p.m. can be estimated as and is equal to , which is approximately 156&deg;F. Finally, the temperature, in &deg;F, at 6:10 p.m. can be estimated as and is equal to , which is approximately 135&deg;F. Since these three given values of m and their corresponding values for can be verified using the function , this is the best function out of the given choices to model the temperature of Kao&rsquo;s hot chocolate after m minutes. Choice A is incorrect because the base of the exponent, , results in the value of increasing over time rather than decreasing. Choice B is incorrect because when m is large enough, becomes less than 70. Choice C is incorrect because the maximum value of at 6:00 p.m. is 115&deg;F, not 185&deg;F.

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