In Newtons Law of Cooling, the constant = 1/k is called the characteristic time. Show that

In Newton’s Law of Cooling, the constant τ = 1/k is called the characteristic time. Show that τ is the time required for the temperature difference (y − T₀) to decrease by the factor e⁻¹ ≈ 0.37. For example, if y(0) = 100°C and T₀ = 0°C, then the object cools to 100/e ≈ 37°C in time τ, to 100/e2 ≈ 13.5°C in time 2τ, and so on.