Final answer:
To find when the temperature of the cake will be 69°F, we can use the formula for exponential decay.
Step-by-step explanation:
To find when the temperature of the cake will be 69°F, we can use the formula for exponential decay:
T = T0 + (T1 - T0)e^(-kt)
where:
T is the temperature at a given time,
T0 is the initial temperature of the cake,
T1 is the final temperature we want,
k is the decay constant, and
t is the time in minutes.
By substituting the given values into the formula, we get:
69 = 241 + (154 - 241)e^(-38k)
Simplifying the equation, we have:
e^(-38k) = (69 - 241) / (241 - 154)
Using natural logarithms, we can solve for k:
-38k = ln[(69 - 241) / (241 - 154)]
k = (1 / -38) * ln[(69 - 241) / (241 - 154)]
Finally, we can substitute the value of k back into the equation to find the time t when the temperature will be 69°F.