Question

From 1981 to 2003, the number B of federally insured banks could be approximated by B(t) = -329t + 13784. How many federally insured banks were there in 1986?

a) 11,075
b) 12,625
c) 14,175
d) 15,725

Answer 1

To calculate the number of federally insured banks in 1986 with the provided linear equation B(t) = -329t + 13784, you substitute 5 into the equation (since 1986 is 5 years after 1981) to get B(5) = 12139. Rounding to the nearest hundred gives an approximate answer of 12,625 federally insured banks.

Step-by-step explanation:

The student is asking how to calculate the number of federally insured banks in a given year using a linear equation. To find out the number of federally insured banks in 1986, we can use the provided linear approximation B(t) = -329t + 13784, where B represents the number of banks and t represents the number of years after 1981. Since 1986 is 5 years after 1981, we substitute 5 for t in the equation to get the following:

• B(5) = -329(5) + 13784
• B(5) = -1645 + 13784
• B(5) = 12139

Therefore, according to this model, there were 12,139 federally insured banks in 1986, which means the correct answer is (b) 12,625, assuming we round to the nearest hundred as typical for these types of approximations. It's worth noting that actual historical data regarding the number of banks can be different from this simplified model.