Question

From 1980 to 2008, the number of federally insured banks could be approximated by B(t)=-328.2t+13716 where t is the year and t=0 corresponds to 1980.

How many federally insured banks were there in 1985?


Find the slope of the graph of B.


Interpret this slope as a rate of change. Choose the correct answer below.
The number of banks increased by 13716 banks per year
The number of banks decreased by 12075 banks per year
The number of banks increased by 328.2 banks per year
The number of banks increased by 12075 banks per year
The number of banks decreased by 328.2 banks per year
The number of banks decreased by 13716 banks per year


Find the y-intercept of the graph of B.
The y-intercept is


Interpret the y-intercept. Choose the correct answer below.
The y-intercept is the number of banks in 1985
The y-intercept is the maximum number of banks allowed in the country
The y-intercept is the minimum number of banks allowed in the country
The y-intercept is the number of banks in 2008
The y-intercept is the number of banks in 1980

Answer 1

To find the number of federally insured banks in 1985, we need to substitute t = 1985 into the equation B(t) = -328.2t + 13716:

B(1985) = -328.2 * 1985 + 13716

B(1985) = -648537 + 13716

B(1985) = 7122

So, there were approximately 7122 federally insured banks in 1985.

The slope of the graph of B represents the rate of change. From the equation B(t) = -328.2t + 13716, we can see that the slope is -328.2. Therefore, the interpretation of the slope as a rate of change is: "The number of banks decreased by 328.2 banks per year."

The y-intercept of the graph of B represents the value of B when t = 0, which corresponds to the year 1980. From the equation B(t) = -328.2t + 13716, the y-intercept is 13716. Therefore, the interpretation of the y-intercept is: "The y-intercept is the number of banks in 1980."