A city health council has modeled the relationship between the number of new COVID-19 cases over time if 80% of residents practice social distancing and wear a mask in public. The relationship can be expressed algebraically as follows, where DaysDays represents the number of days from today.

Cases= 10,000 100Days1.4Cases= 10,000 100Days1.4

Based on the model, if 80% of residents practice social distancing and wear a mask in public, how many days will it take for the number of new cases to be less than 5000?

days