The number of banks in a country for the years 1935 through 2009 is given by the following function. \( f(x)=\left\{\begin{array}{r}84.8 x+12,365 \text { if } x<90 \\ -376.3 x+48,686 \text { if } x \geq 90\end{array}\right. \), where \( x \) is the number of years after 1900 Complete parts (a)-(b). a) What does this model give as the number of banks in \( 1970 ? 1990 ? 2020 \) ? The number of banks in 1970 is

To find the number of banks in the years 1970, 1990, and 2020 using the given function, we first determine the corresponding values of \( x \). - For 1970: \( x = 70 \) (1970 - 1900) - For 1990: \( x = 90 \) (1990 - 1900) - For 2020: \( x = 120 \) (2020 - 1900) Now we can calculate: 1. **For 1970** (\( x = 70 \)): Since \( x < 90 \): \[ f(70) = 84.8(70) + 12,365 \] \[ = 5,936 + 12,365 \] \[ = 18,301 \] So, the number of banks in 1970 is **18,301**. 2. **For 1990** (\( x = 90 \)): Since \( x \geq 90 \): \[ f(90) = -376.3(90) + 48,686 \] \[ = -33,867 + 48,686 \] \[ = 14,819 \] So, the number of banks in 1990 is **14,819**. 3. **For 2020** (\( x = 120 \)): Since \( x \geq 90 \): \[ f(120) = -376.3(120) + 48,686 \] \[ = -45,156 + 48,686 \] \[ = 3,530 \] So, the number of banks in 2020 is **3,530**. In summary: - The number of banks in 1970 is **18,301**. - The number of banks in 1990 is **14,819**. - The number of banks in 2020 is **3,530**.