Mathematics, 15.03.2020 18:54 cecilysimpson7521

6. A liquid is taken out of a refrigerator and placed in a warmer room, where its temperature, in °F)
increases over time. It can be modeled using the equation T(m) = 74 - 39(0.87)".
b. What is the initial tomperature of the liquid?
initas temp = 74°F
c. How many minutes, to the nearest tenth, does it take for the temperature to reach 50°F ? Solve
algebraically

Answers: 1

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Answer from: amflet19

(A) In the given equation, m is the time in minutes and T(m) represents the temperature in Fahrenheit of the liquid.

(b) The initial value of temperature is 35 Degrees Fahrenheit.

(A)

The equation of temperature model is, $T(m)=74-39(0.87)^{m}$ .

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,

$T(0) = 74 -39(0.87)^{0}\\T(0)= 74-39\\T(0)=35 \;\rm ^{\circ}F$

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.

$T(m)=74-39(0.87)^{m}\\\\50=74-39(0.87)^{m}\\\\39(0.87)^{m}=74-50\\\\ln(0.87)^{m}=ln((74-50)/39)\\\\m=\dfrac{ln(0.615)}{ln(0.87)} \\\\m=3.50 \;\rm min$

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

Answer from: chaseashley24

b) 35 °F

c) 3.5 minutes

Step-by-step explanation:

The temperature of the liquid is modeled using the following equation:

$T(m)=74-39(0.7)^{m}$

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.

$T(0)=74-39(0.87)^{0}\\\\ T(0)=35$