Question

a cup of 205° coffee on a table in a 72° room loses approximately 15% of its temperature every minute until it reaches room temperature. the resulting exponential model for the temperature, t, after m minutes can be approximated by the model t = 133(0.85)^m + 72. what is the temperature after 13 minutes? round your answer to the nearest whole degree.

Explanation:

Step1: Substitute m = 13

Substitute m = 13 into the formula $t = 133(0.85)^m+72$, we get $t = 133(0.85)^{13}+72$.

Step2: Calculate $(0.85)^{13}$

Using a calculator, $(0.85)^{13}\approx0.1216$.

Step3: Calculate $133\times(0.85)^{13}$

$133\times0.1216 = 16.1728$.

Step4: Calculate t

$t=16.1728 + 72=88.1728$.

Step5: Round the result

Rounding 88.1728 to the nearest whole - degree gives 88.

Answer:

88