Metro Department Store found that t weeks after the end of a sales promotion the volume of sales was given by S(t) = B + Ae-kt (0 stS 4) where B = 41,000 and is equal to the average weekly volume of sales before the promotion. The sales volumes at the end of the first and third weeks were $82,050 and $63,400, respectively. Assume that the sales volume is decreasing exponentially. (a) Find the decay constant k. (Round your answer to five decimal places.) k = (b) Find the sales volume at the end of the fourth week. (Round your answer to the nearest whole number.)
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.
Please explain every step I have tried 3 EXPERTS but none have given an explanation on what e is.
EXAMPLE
Q(24.6)=450e^-0.0488(24.6)
when you reach the final step of find the sales volume at the end of the fourth week can you PLEASE EXPLAIN HOW YOU MULTIPLY OUT THE FORMULA AND WHAT E IS AND HOW DO YOU GET E
that formula above me was just an example to show you what I'm talking about please help nobody has helped yet
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