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P3 help T = Ae^(-kt)

q 38 rev ex 1

The rate of cooling of a metal ball placed in melting ice is proportional to its own temperature T

at time t

T = Ae^(-kt)

A and k positive constants

The temperature of the metal ball falls from 50 to 40 deg in twenty seconds. Find its temperature at the end of the next twenty seconds
Reply 1
BLUREMI
q 38 rev ex 1

The rate of cooling of a metal ball placed in melting ice is proportional to its own temperature T

at time t

T = Ae^(-kt)

A and k positive constants

The temperature of the metal ball falls from 50 to 40 deg in twenty seconds. Find its temperature at the end of the next twenty seconds


when t = 0s, 50= Ae^(0)

so A= 50
and when t = 20,

40=50e^(-20k)

k=0.0111571775....

so when t=40

T=50e^(-0.011157*40)
T= 32 deg