Answer:
65
Step-by-step explanation:
You can use f(15) = 40 to solve for C, then find f(0), the initial temperature.
40 = f(15)
40 = Ce^(-0.045·15) +14 = .50916C +14
26 = .50916C
26/.50916 = C ≈ 51.065
Then f(0) is ...
f(0) = 51.065·e^0 +14 = 65.065 ≈ 65
The initial temperature of the water was 65 degrees Fahrenheit.
Answer:
23
Step-by-step explanation:
data
[tex]f(15)= 40\\t= 15\\ C=?\\t_0=0[/tex]
[tex]t_0=0[/tex] because it's the initial time, when we start counting
To know how much the temperature is worth in the initial time[tex]t_0=0[/tex] we must find out the value of the constant C with the data we have of the situation at 15 minutes
[tex]f(t)= Ce^{(-kt)}+14\\t=15\\f(15)= Ce^{(-k(15))}+14\\40= Ce^{-((0.045)(15))}+14\\40-14= Ce^{-0.675}\\\frac{26}{e^{-0.675}} = C \\8.89=C[/tex]
Find the initial temperature by replacing the data given and obtained
[tex]f(t)= Ce^{(-kt)}+14\\t=0\\f(0)= Ce^{(-k(0))}+14\\f(0)= 8.89(1)+14\\f(0)= 22.89\\f(0)= 23[/tex]
