At 10: 00 am, rick arrived at the location of a gromflomite who had died. the temperature of thelocation was 64°f, and at the time of death, the body temperature of the gromflomite was 85.3°f. rick took the body’s temperature at 10: 30 am, at which time it was 76.3°f, and then againat 11: 00 am, at which the temperature was 72.7°f. at what time did the gromflomite die? [round answer to the nearest minute.]

the time of death td= 9:42 am

Step-by-step explanation:

If we suppose that a mass of constant heat capacity is cooled at a rate that is proportional to the temperature difference between the body and the environment then we can use an exponencial model for the body temperature as

T - T env = a*e^(-t/b)

then

if we use the reference t=0 as 10:30 am , then at t=0 , T= 76.3°F and

T - T env = a*e^(-t/b)

76.3°F-64°F = a*e^(-0/b)

a = 76.3°F-64°F = 12.3 °F

then for  t= 0.5 hours (11:00 am from 10:30 am) ,T= 72.7°F and

T - T env = a*e^(-t/b)

72.7°F - 64°F = 12.3 °F*e^(-0.5 h /b)

b = -0.5 h/ln [( 72.7°F - 64°F) / 12.3 °F ] = 1.44 h

finally for Td=85.3°F the time of death td= is

Td - T env = a*e^(-td/b)

td= -b* ln[(Td - T env)/a]

td= - 1.44 h * ln[(85.3 °F - 64°F )/12.3 °F ] ]= - 0.79 h from 10:30 am

therefore

td= - 0.79 h*60 min/hour= -47.4 min from 10:30 am = 9:42 am

Note :

we applied the following physical model to end with the exponencial function

Q= m*c * (T-To) → dQ/dt= m*c*dT/dt

and -dQ/dT= U*A*(T- T env)

then

m*c*dT/dt =  -U*A*(T- T env)

-dT/dt = U*A/(m*C) *(T - T env)

ln ( T- T env) = U*A/(m*C) (-t) + C

T- T env = e^(U*A/(m*C) t + C) = e^[U*A/(m*C)*(-t)] *e^C

T- T env = a*e^(-t/b)

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation:

step-by-step explanation:

im not sure what the answer is