An object cools according to

MATHEMATICS · Single correct · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

T=T_0 e^{kt}

, where

T

is the temperature (°C) at time

t

minutes. Measurements show

T(2)=75

and

T(5)=60

. Assuming both measurements satisfy the same exponential model, which of the following is the best estimate of the initial temperature

T_0

t=0

? (a)

85\,^{\circ}\text{C}

(b)

87\,^{\circ}\text{C}

(c)

65\,^{\circ}\text{C}

(d)

75\,^{\circ}\text{C}