Practise fitting half-life, logarithmic, sinusoidal, logistic or piecewise models, interpreting parameters, making domain-valid predictions and judging extrapolation.
George is researching the growth in the number of electric vehicles (EVs) in the European Union in order to investigate some of the difficulties that might arise if the target of banning sales of all petrol and diesel cars in 2035 is to be met.
George begins his research by predicting how many electric vehicles (EVs) will be in the European Union in 2035.
The number of EVs in the European Union, N, measured in millions, is shown in the following table. The time t is measured in years from the beginning of 2016 where .
George models this data set using the logistic function , where .
In context, explain the significance of 310 in George's logistic function.
Use the value of N at t=1 to show that .
Use the value of N at t=7 to find a second expression for C.
Use your answers to part (b) to find a value for
.
C.
George uses his model to predict values of N at the end of the years 2017 to 2021. These values are shown in the following table, correct to one decimal place.
Calculate the value of a correct to one decimal place.
Use the model to predict the number of EVs in the European Union at the end of 2035.
One of the main difficulties in meeting the European Union's target is the provision of sufficient public charging points.
The European Union estimates that 80 % of car owners will be able to charge their cars at home and the remaining 20 % will require public charging points. It is planned to have one public charging point for every 10 cars that require them.
Use George's model to find an expression for the total number of public charging points required at time t.
At the end of 2020 there were 0.22 million public charging points in the European Union and at the end of 2022 there were 0.54 million.