SOLUTION: Hi, this is the question I would love help on:
A patient suffers from a short fever. Their body temperarure is normally 37.4 degrees celcius but during the fever, it is given by
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-> SOLUTION: Hi, this is the question I would love help on:
A patient suffers from a short fever. Their body temperarure is normally 37.4 degrees celcius but during the fever, it is given by
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Question 1044555: Hi, this is the question I would love help on:
A patient suffers from a short fever. Their body temperarure is normally 37.4 degrees celcius but during the fever, it is given by the function:
y(t) = -0.01t^2 + 0.3e^t + 37.4 (t is greater than or equal to 0)
where t is the number of hours since the onset of the fever.
1. What is the average rate of change of temperature y(t) at t=2 and t=6
2. How fast is the body temperature changing after 3 hours?
Thank you! Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! We need the first derivative of y(t) to give us rate of change
:
y(t) = -0.01t^2 + 0.3e^t + 37.4
:
using the power rule and the fact that the derivative of e^t is e^t
:
y'(t) = 0.3e^t -0.02t
:
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y'(2) = 0.3e^2 -0.04 = 0.3(7.39) -0.04 = 2.177 approx 2.18
y'(6) = 0.3e^6 -0.12 = 120.908 approx 120.91
:
y'(3) = 0.3e^3 -0.06 = 5.965 approx 5.97
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