The temperature of water ( $w∘Cw^\circ\text{C}$ ) in a kettle $t\,$ minutes after it was boiled is recorded in the table below


$t$	1	3	6	9	11	15	20
$w$	92	76	65	50	46	33	25

The data is coded using the changes of variable $x = t$ and $y = \log_{10} w$

The regression line of $x\,$ on $y\,$ is found to be $y = 1.99 - 0.031 x$

Given that the data can be modelled by an equation in the form $w = ab^t$ where $a\,$ and $b\,$ are constants. Find the values of $a\,$ and $b\,$ to 3 significant figures.

Give an interpretation of the constant $a\,$ in this equation.

Explain why this model is not reliable for calculating the temperature after 1 hour.

The temperature of water ( $w∘Cw^\circ\text{C}$ ) in a kettle $t\,$ minutes after it was boiled is recorded in the table below


$t$	1	3	6	9	11	15	20
$w$	92	76	65	50	46	33	25

The data is coded using the changes of variable $x = t$ and $y = \log_{10} w$

The regression line of $x\,$ on $y\,$ is found to be $y = 1.99 - 0.031 x$

Given that the data can be modelled by an equation in the form $w = ab^t$ where $a\,$ and $b\,$ are constants. Find the values of $a\,$ and $b\,$ to 3 significant figures.

Give an interpretation of the constant $a\,$ in this equation.

Explain why this model is not reliable for calculating the temperature after 1 hour.

1.8 Exponentials and Logarithms

Question 15

Markscheme

1.8 Exponentials and Logarithms

Question 15

Markscheme

1.8 Exponentials and Logarithms

Question 15

1.8 Exponentials and Logarithms Questions

1.8 Exponentials and Logarithms

Question 15

1.8 Exponentials and Logarithms Questions