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Estabon poured himself a hot beverage that had a temperature of 199 Fahrenheit then set it on the kitchen table to cool. The temperature of the kitchen was a constant 71 Fahrenheit. If the drink cooled to 176 Fahrenheit in 4 minutes, how long will it take for the drink to cool to 96 Fahrenheit? PLEASE HELP ME

Respuesta :

MissPhiladelphia

This can be solve using newtons law of cooling

T – Ts = (To – Ts)* (e^(-kt))

Where Ts is the ambient temperature

To is the initial temperature

T is the temperature at time t

t is time

k is constant

so at To = 199 F, T = 176 F , t = 4 min, Ts = 71

so solve the k

( 176 – 71) = ( 199 – 71)*e^(-4k)

K = 0.00495

So t =? T = 96 F

( 96 – 71) = ( 199 – 71)*e^(-0.00495t)

Solve for t

t =329 min