Final answer:
The slope in the given model is 'n', which represents the rate at which refineries increase each year. The y-intercept is 0, meaning at time t=0, the model starts with no refineries. Without a concrete value for 'n', specific predictions for the number of refineries can't be made.
Step-by-step explanation:
The slope of a model representing the number of oil refineries, nt, with n being the number of refineries and t being the years, is given by the coefficient of t. In this case, the slope is n, which indicates the rate of change in the number of refineries per year. It suggests how many additional refineries are constructed each year. For this model, there is no specific numeric value given to the slope; it is simply represented by n, which would vary depending on the given data.
The y-intercept is the value of the nt model when t is 0. As the model is nt, the y-intercept is 0. This means that at time t=0, the number of refineries would also be 0 if we are strictly following the model, which may not reflect reality if there were already existing refineries when the observations began.
The prediction for the number of refineries at a specific time cannot be made without a specific value for n. If n were known, we could calculate it by simply multiplying n by the desired t value (the number of years in the future for the prediction).