Whats the best possible way to represent a time as a double type

I am trying to use a library called QCustomPlot and on the X Axis I want to be able to put the users time zone of the stock market being open, from say 9:30AM to 4:00PM but the paramenters i need when setting the range of the x axis has to be a double, what is the best way about getting the time to a format I can use? Thank you in advance!

Extra: Also is there any easy way to make it where the range of the y axis will go up and down depending on where the current price of the underlying stock is?

Code:

string symbol_std = symbol.toStdString();


    //Retrieves json format of data
    Json::Value chartData = IEX::stocks::chartYtd(symbol_std);

    //Size of json
    int n = chartData.size();

    //Stores x and y values
    QVector<double> time(n), average(n);


    QDateTime start = QDateTime(QDate(2020, 1, 1));
    start.setTimeSpec(Qt::UTC);
    double startTime = start.toTime_t();
    double binSize = 3600*24;
    time[0] = startTime;

    //Reads in data from json(historical data 1 day delayed)
    for(int i = 0; i < chartData.size(); i++)
    {
        time[i + 1] = startTime + 3600*(i+1);
        average[i] = (chartData[i]["close"].asDouble());

        if((average[i] == 0) && (time[i] != chartData.size() - 1))
        {
            average[i] = average[i-1];
        }


    }
    //Initializes graph
    ui->stockGraph->addGraph();
    ui->stockGraph->graph(0)->setData(time, average);

    // give the axes some labels:
    ui->stockGraph->xAxis->setLabel("Time");
    ui->stockGraph->yAxis->setLabel("Price");

    // set axes ranges, so we see all data:
    ui->stockGraph->xAxis->setRange(time[0], time[n]);
    ui->stockGraph->yAxis->setRange(210, 340);
    ui->stockGraph->replot();

Visual of Graph

what is the best way about getting the time to a format I can use?

You need a QwtDateScaleEngine along with a QwtDateScaleDraw. These will interpret your double values as the time from the epoch "1970-01-01T00:00:00 UTC" in milliseconds.

ui->stockGraph->setAxisScaleDraw(QwtPlot::xBottom, new QwtDateScaleDraw());
ui->stockGraph->setAxisScaleEngine(QwtPlot::xBottom, new QwtDateScaleEngine());