The market value $V$ , in pounds (£), of a limited-edition bronze sculpture is modelled by the equation

V = pq^t

where $t$ is the number of years since its initial release and $p$ and $q$ are constants.

A researcher records the market value over several years. The graph of $log_{10} V$ against $t$ is a straight line that passes through the points $(0, 3.15)$ and $(12, 5.07)$ .

Determine an equation for this line in the form $log_{10} V = mt + c$ .

Calculate the value of $p$ and the value of $q$ , giving your answers to 3 significant figures.

Use the model to estimate the number of years, $t$ , until the sculpture reaches a value of £50,000.

The market value $V$ , in pounds (£), of a limited-edition bronze sculpture is modelled by the equation

V = pq^t

where $t$ is the number of years since its initial release and $p$ and $q$ are constants.

A researcher records the market value over several years. The graph of $log_{10} V$ against $t$ is a straight line that passes through the points $(0, 3.15)$ and $(12, 5.07)$ .

Determine an equation for this line in the form $log_{10} V = mt + c$ .

Calculate the value of $p$ and the value of $q$ , giving your answers to 3 significant figures.

Use the model to estimate the number of years, $t$ , until the sculpture reaches a value of £50,000.

1.6 Exponentials and logarithms

Question 56

Markscheme

1.6 Exponentials and logarithms

Question 56

Markscheme

1.6 Exponentials and logarithms

Question 56

1.6 Exponentials and logarithms Questions

1.6 Exponentials and logarithms

Question 56

1.6 Exponentials and logarithms Questions