From 1987 to 2007, the number B of federally insured banks could be approximated by B(t)=-323t+13708 where t is the year and t=0 corresponds to 1987. 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 -323 banks per year The number of banks decreased by 323 banks per year The number of banks decreased by 13708 banks per year The number of banks increased by 13708 banks per year The number of banks decreased by -323 banks per year The number of banks increased by 323 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 2007 The y-intercept is the number of banks in 1992 The y-intercept is the number of banks in 1987 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
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
From 1987 to 2007, the number B of federally insured banks could be approximated by B(t)=-323t+13708
where t is the year and t=0 corresponds to 1987.
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 -323 banks per year
The number of banks decreased by 323 banks per year
The number of banks decreased by 13708 banks per year
The number of banks increased by 13708 banks per year
The number of banks decreased by -323 banks per year
The number of banks increased by 323 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 2007
The y-intercept is the number of banks in 1992
The y-intercept is the number of banks in 1987
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
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