From 1985 to 2007, the number B B of federally insured banks could be approximated by B ( t ) = − 329.4 t + 13747 B(t)=-329.4t+13747 where t is the year and t=0 corresponds to 1985. How many federally insured banks were there in 1990?

The number of federally insured banks in the year 1990 was 12,100.

Given data:

To find the number of federally insured banks in the year 1990, you need to substitute the value of t = 1990 into the given function B(t):

B(t) = -329.4t + 13747

Since t corresponds to the year and t = 0 corresponds to 1985, we need to calculate for t = 1990 - 1985.

t = 5.

Substitute t = 5 into the function:

B(5) = -329.4 * 5 + 13747

Now, perform the calculations:

B(5) = -1647 + 13747

B(5) = 12100

Hence, there were approximately 12,100 federally insured banks in the year 1990.

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Final answer:

Using the given equation and by substituting t with 5 (for the year 1990, five years after 1985) in that equation, we find that there were 13363 federally insured banks in 1990.

Explanation:

The question is asking how many federally insured banks there were in 1990, given that the number of banks in any given year from 1985 to 2007 is given by the equation

B(t) = -329.4t + 13747

. In this equation,

t

is the year with t=0 corresponding to 1985. To find the answer, we should substitute in the appropriate value of t, which would be 5 because 1990 is five years after 1985. Thus, the equation becomes B(5) = -329.4*5 + 13747. This simplifies to 15010 - 1647, which equals

13363

. Therefore, there were 13363 federally insured banks in 1990.

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