A can of soda at 80°F is placed in a refrigerator that maintains a constant temperature of 37°F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by
T(t) = 37 + 43e−0.058t.
Whats the Question?
Supose you want the soda at 41ºF(5ºC), then:
41=37+43e-0,058t
4=43e-0,058t
e-0,058t=0,093 or 1/e0,058t=0,093
e0,058t = 10,75
0,058t 0 ln 10,75
t=2,375/0,058
Finally t=40,95 min
To find the temperature of the soda t minutes after it is placed in the refrigerator, we can use the provided formula:
T(t) = 37 + 43e^(-0.058t)
Here's how to calculate the temperature of the soda at different time intervals:
1. Calculate the temperature of the soda when it is placed in the refrigerator (t = 0):
To find the temperature at t = 0, substitute t = 0 into the equation:
T(0) = 37 + 43e^(-0.058(0))
T(0) = 37 + 43e^0
T(0) = 37 + 43 * 1
T(0) = 37 + 43
T(0) = 80°F
Therefore, when the soda is initially placed in the refrigerator, its temperature is 80°F.
2. Calculate the temperature of the soda after a specific time interval:
To find the temperature at a specific time interval (t), substitute the value of t into the equation:
For example, if we want to find the temperature after 5 minutes (t = 5):
T(5) = 37 + 43e^(-0.058(5))
T(5) = 37 + 43e^(-0.29)
T(5) ≈ 37 + 43 * 0.747
T(5) ≈ 37 + 32.121
T(5) ≈ 69.121°F
Therefore, after 5 minutes, the temperature of the soda would be approximately 69.121°F.
You can repeat this process to find the temperature at different time intervals by substituting the desired values of t into the equation.