The temperature T(t)°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 evaluate the function at time t = 0:

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

This simplifies to: $T(0) = 15 + 4e^{0}$

Since $e^{0} = 1$, we have: $T(0) = 15 + 4(1)$

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

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

The correct answer is D. 19.