Question

The number of banks in a country for the years 1935 through 2009 is given by the following function.

f(x) = 84.5x+12,367 if x < 90)
= - 376.6x + 48,689 if x >=90
where x is the number of years after 1900
What does this model give as the number of banks in 1970?

Answer 1

The given function predicts a negative number of banks in 1970, which doesn't make sense. Extrapolation beyond the range of x values is not reliable.

Step-by-step explanation:

The given function is:

f(x) = 84.5x + 12,367 if x < 90

f(x) = -376.6x + 48,689 if x >= 90

To find the number of banks in 1970, we need to substitute x = 1970 into the second part of the function since 1970 is greater than or equal to 90.

Substituting x = 1970, we have:

f(1970) = -376.6(1970) + 48,689

f(1970) = -739,982 + 48,689

f(1970) = -691,293

The model predicts that there would be -691,293 banks in 1970. However, this answer doesn't make sense because the number of banks cannot be negative. Additionally, the given function is extrapolating beyond the range of x values, which is not reliable.