A quantity of ethanol was heated until it reached boiling point - Edexcel - A-Level Maths Pure - Question 11 - 2020 - Paper 2

To determine the values of A and B, we substitute the given temperatures into the equation:

1. At time t = 0 seconds, θ = 18 °C:

   Thus,

   $$18 = A - B e^{-0.07(0)}$$

   This simplifies to:

   $$18 = A - B$$

   (Equation 1)

2. At time t = 10 seconds, θ = 44 °C:

   Thus,

   $$44 = A - B e^{-0.07(10)}$$

   This simplifies to:

   $$44 = A - B e^{-0.7}$$

Using $e^{-0.7} ext{ (approximately 0.496)}$, we rewrite it as:

$$44 = A - 0.496B$$

(Equation 2)

3. Now solving these equations:

From Equation 1: $A = 18 + B$

Substituting into Equation 2:

$44 = (18 + B) - 0.496B$

This leads to:

$44 = 18 + B - 0.496B$

Simplifying gives:

$B - 0.496B = 44 - 18$

$0.504B = 26$

Thus,

B = rac{26}{0.504} ext{ (approximately 51.6)}

4. Now substituting B back into the first equation:

$A = 18 + 51.6$

Which gives:

$A = 69.6$

Therefore, the complete equation is:

$θ = 69.6 - 51.6e^{-0.07t}$