Answer:
b) 35 °F
c) 3.5 minutes
Step-by-step explanation:
The temperature of the liquid is modeled using the following equation:
[tex]T(m)=74-39(0.7)^{m}[/tex]
Here, m is the time in minutes and T(m) represents the temperature in Fahrenheit of the liquid after m minutes.
b) Initial Temperature of the Liquid.
When the liquid is just taken out of the refrigerator the time m is equal to 0. So, substituting m = 0 in given equation will give us the Initial temperature of the Liquid.
[tex]T(0)=74-39(0.87)^{0}\\\\ T(0)=35[/tex]
This means, the initial temperature of the liquid was 35 °F.
c) Time taken to reach 50 °F
In order to find the time, in minutes, it will take to reach 50°F, we replace T(m) by 50 and find the corresponding value of m.
[tex]50=74-39(0.87)^{m}\\\\ 39(0.87)^{m}=74-50\\\\ 39(0.87)^{m}=24\\\\ (0.87)^{m}=\frac{24}{39}[/tex]
Taking log of both sides, we get:
[tex]log (0.87)^{m}=log(\frac{24}{39})\\\\ m \times log(0.87)=log(\frac{24}{39})\\\\m=log(\frac{24}{39}) \times \frac{1}{log(0.87)}\\\\ m=3.5[/tex]
Thus, it will take 3.5 minutes to reach 50°F.
(A) In the given equation, m is the time in minutes and T(m) represents the temperature in Fahrenheit of the liquid.
(b) Â The initial value of temperature is 35 Degrees Fahrenheit.
(c)  The required time at the nearest tenth, to take for the temperature to reach 50°F is 3.50 minutes.
(A)
The equation of temperature model is, [tex]T(m)=74-39(0.87)^{m}[/tex].
Here m is the time in minutes and T(m) represents the temperature in Fahrenheit of the liquid after m minutes.
(b)
When the liquid is just taken out of the refrigerator the time m is equal to 0. So, substituting m = 0 in given equation will give us the Initial temperature of the Liquid. Then the equation becomes,
[tex]T(0) = 74 -39(0.87)^{0}\\T(0)= 74-39\\T(0)=35 \;\rm ^{\circ}F[/tex]
Thus, we can conclude that the initial value of temperature is 35 Degrees Fahrenheit.
(c)
In order to find the time, in minutes, it will take to reach 50°F, we replace T(m) by 50 and find the corresponding value of m.
[tex]T(m)=74-39(0.87)^{m}\\\\50=74-39(0.87)^{m}\\\\39(0.87)^{m}=74-50\\\\ln(0.87)^{m}=ln((74-50)/39)\\\\m=\dfrac{ln(0.615)}{ln(0.87)} \\\\m=3.50 \;\rm min[/tex]
Thus, we can conclude that the required time at the nearest tenth, to take for the temperature to reach 50°F is 3.50 minutes.
Learn more about the linear model here:
the nearest tenth, does it take for the temperature to reach 50°F
