The temperature $T(t)^{ ext{o}}C$ of an object at time $t$ seconds is modelled using Newton’s Law of Cooling - HSC - SSCE Mathematics Extension 1 - Question 1 - 2023 - Paper 1

To find the initial temperature of the object, we need to evaluate the function $T(t)$ at time $t = 0$.

Substituting $t = 0$ into the equation:

$T(0) = 15 + 4e^{-3 imes 0}$

This simplifies to:

$T(0) = 15 + 4e^{0}$

Since $e^{0} = 1$, we have:

$T(0) = 15 + 4 imes 1$

Thus, the expression becomes:

$T(0) = 15 + 4 = 19$

Therefore, the initial temperature of the object is 19°C.