Investigation: Logarithms (HSC SSCE Mathematics Advanced): Flashcards

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Investigation: Logarithms
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Newton's cooling formula

T(t)=Tenv+(T0−Tenv)e−ktT(t) = T_{env} + (T_0 - T_{env})e^{-kt}

T(t)T(t) in Newton's cooling formula

Temperature of the body at time tt

TenvT_{env} in Newton's cooling formula

Temperature of the surrounding environment

T0T_0 in Newton's cooling formula

Initial temperature of the body

kk in Newton's cooling formula

A constant that depends on the specific situation

Notation for natural logarithm (base ee)

ln⁡\ln

Relationship between logarithms and exponentials

Logarithms are the inverse of exponential functions

Pattern of body cooling over time

Exponential, not linear

Cooling rate behaviour over time

Rapid at first, then slows down

Average living body temperature

Approximately 37°C

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