A can of soda is placed inside a cooler. As the soda cools, its temperature T(x) in degrees Celsius is given by the following exponential function, where is the number of minutes since the can was placed in the cooler.
T(x)=-22+44e^-0.03x
Find the initial temperature of the soda and its temperature after 18 minutes. Round your answers to the nearest degree as necessary.
Initial temp=
After 18 minutes =
T(x) = -22 + 44*e^(-0.03x).
T(o) = -22 + 44*e^(-0.03*0),
T(o) = -22 + 44*e^0 = -22 + 44*1 = 22deg C.
T(18) = -22 + 44*e^(-0.03*18),
T(18) = -22 + 44*0.5827 = 4 deg C.
T(x) =
A can of soda is placed inside a cooler. As the soda cools, its temperature
Tx
in degrees Celsius is given by the following function, where
x
is the number of minutes since the can was placed in the cooler.
T(x) = -17+39e^-0.45
poop= T (x) = - 17 + 39e^-0.45
To find the initial temperature of the soda, we can substitute x = 0 into the equation T(x) = -22 + 44e^(-0.03x):
T(0) = -22 + 44e^(-0.03(0))
Since e^0 = 1, the equation simplifies to:
T(0) = -22 + 44(1)
T(0) = -22 + 44
T(0) = 22
Therefore, the initial temperature of the soda is 22 degrees Celsius.
To find the temperature after 18 minutes, we can substitute x = 18 into the same equation:
T(18) = -22 + 44e^(-0.03(18))
The value of e^(-0.03(18)) can be calculated as follows:
e^(-0.03(18)) = e^(-0.54)
Using a scientific calculator, we find that e^(-0.54) is approximately 0.582, rounded to three decimal places.
Substituting this value back into the equation, we have:
T(18) = -22 + 44(0.582)
T(18) = -22 + 25.5284
T(18) ≈ 3.53
Therefore, the temperature of the soda after 18 minutes is approximately 3.53 degrees Celsius, rounded to two decimal places.