A city currently has 60 family-owned restaurants. In the future, it is estimated that the number of those restaurants will decline at a rat of 18% per year. Based on that estimate, what is the fewest number of years it will take for there to be less than 20 family-owned restaurants in the city? A.1 B. 3 C. 4 D. 6

To know precisely how the number of restaurants in the city decreases over time, it is necessary to determine the 18% of the total of restaurants each year and to subtract this number. The process year per year is shown below:

First-year- 60 restaurants- Find the percentage by writing the known value and using cross multiplication

[tex]60 = 100[/tex] %

[tex]x = 18[/tex]%

[tex]x 100 = 60 x 18[/tex]

[tex]x = \frac{1080}{100}[/tex]

[tex]x = 10.8[/tex] Number of restaurants that were closed

[tex]60-10.8 = 49.2[/tex] New total

Second-year - 49.2 restaurants- Repeat te process

[tex]x = \frac{49.2x 18}{100}[/tex] Shortened version of the equation. Total of restaurants, multiplied by percentage and divided into 100 (total percentage)

[tex]x = 8.8[/tex]

[tex]49.2 - 8.8 = 40.4[/tex] New total

Third-year- 40.4 restaurants

[tex]x = \frac{40.4 x 18}{100}[/tex]

[tex]x = 7.2[/tex]

[tex]40.4-7.2 = 33.2[/tex] New total

Fourth-year- 33.2 restaurants

[tex]x = \frac{33.2x 18}{100}[/tex]

[tex]x = 6.3[/tex]

[tex]33.2- 6.3= 26.9[/tex] New total

Fifth-year- 26.9 restaurants

[tex]x = \frac{26.9 x 18}{100}[/tex]

[tex]x = 4.8[/tex]

[tex]26.9-4.8 = 22.1[/tex] New total

Sixth-year- 22.1 restaurants

[tex]x = \frac{22.1x 18}{100}[/tex]

[tex]x= 3.96[/tex]

[tex]22.1-3.9 = 18.1[/tex]

According to this at this rate, it will take at least 6 years for the number of restaurants to be below 20.