Question 1129730
<font color="black" face="times" size="3">Here are some thoughts as to why you may have the wrong answer
<ul>
<li>Scenario #1: You forgot to put a lowercase t in the exponent for the term e^( (-0.0103 ) )</li>
<li>Scenario #2: You rounded the decimal value for k in the incorrect format (eg: you rounded to 4 decimal places but maybe your teacher wanted 6 instead)</li>
</ul>


Assuming that only scenario #1 applies, then the temperature T(t) function is approximately:
<font color=red>T(t)= 35*e^(-0.0103*t)+65</font>
You do not need two sets of parenthesis. The asterisk symbols indicate multiplication which may be omitted depending on the computer system your teacher uses.


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As a way to check the answer, let's plug in t = 0 and see what happens


T(t)= 35*e^(-0.0103*t) + 65
T(0)= 35*e^(-0.0103*0) + 65 .... replace every lowercase t with 0; use PEMDAS to simplify
T(0)= 35*e^(0) + 65
T(0)= 35*1 + 65
T(0)= 35 + 65
T(0)= 100

As expected, we get a result of 100. So when the time is t = 0 minutes (aka the starting point), the temperature is T = 100 degrees Fahrenheit. This is part 1 of confirming the answer.


Onto part 2: Plug in t = 15. We should get T = 95

T(t)= 35*e^(-0.0103*t) + 65
T(15)= 35*e^(-0.0103*15) + 65 ... replace every t with 15
T(15)= 35*e^(-0.1545) + 65
T(15)= 35*0.856843492142097 + 65 .... this is approximate
T(15)= 29.9895222249734 + 65
T(15)= 94.9895222249734
If you round to the nearest tenth or the nearest whole number, then you'll get approximately T(15) = 95. Due to rounding error, the 94.9895222249734 should be a lot closer to 95 (or close enough that the calculator can't determine the difference). This concludes showing how after t = 15 minutes, the temperature is now approximately T = 95 degrees F. 


These two parts help verify that the formula <font color=red>T(t)= 35*e^(-0.0103*t)+65</font> is the correct function your teacher wants. Or at least, it's a good approximation of the function.


Side Note: it's unfortunate that T shows up as the temperature and t is the time, which in my opinion is a bit confusing. It would be more helpful to only use t once. If t is the time, then H could represent the temperature (H for heat maybe) making the function to be H(t)= 35*e^(-0.0103*t) + 65. However, your teacher is using uppercase T for temperature so it's best to stick with that so you don't lose points.</font>