A particular type of cell doubles in number every hour. Which function can be used to find the number of cells present at the end of h hours if there are initially 8 of these cells? REMEMBER – Anything to the zero power is one and anything to the power of one is that thing. So when time (x) is 0 it makes the equation equal the initial number. On=8(2)" On=8()" On=8+(2)" On= 8+

Q: A cat is falling from a branch. Its height t seconds after it fell is given by the function h(t) =…

A: We have given height  ht=-16t2+5 To get for what height cat was falling  Put t=0 h0=0+5 h0=5 height…

Q: find the equation of the inverse of one-to-one function  x^2 +9 , x≥0

A:

Q: If the function y = ln(3) · ()4 is expressed as a power function in the form y = k · xº , then what…

A: Solve and compare

Q: Differentiate the function. y = ex + 3 + 8

A: We have to differentiate the given function.

Q: For an exponential fuction in the form f(×)=ab^×what does the value of a and b represent A. a…

A: In the question it is asked to write about variables a and b in function f(x)=abx.

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT PLEASE Derive the following functions 32. y=(x²-5x)(x²-3x) 34.…

A:

Q: (x-4)² The curve for f(x) = -- - 1 is shown in blue in the graph below. Drag the movable blue point,…

A: The given function is fx=-x-422-1.   The condition for the existence of the inverse of a function fx…

Q: When two odd functions are multiplied, the combined function is also an odd function.     True or…

A: Given statement is, when two odd functions are multiplied, the combined function is also an odd…

Q: State Odd and Even Functions Under Multiplication ?

A: Let f:D→R be a function, Then f is said to be even function if f-x=fx ∀ x∈D and  f is said to be odd…

Q: exp(x) = ex ?  Is it just a matter of notation, or does exp( ) mean something else?

A: Yes this is true exp(x) = e^x  exp(x) is command in coding language to type e^x

Q: (10x-19) (3r + 2) (5x-3)

A: We will use the exterior angle property of a triangle that states that an exterior angle is equal to…

Q: Tell which of the following functions has been vertically translated 8 up. y = 5 * e*-8 – 2 y = -5 *…

A: Given four function.

Q: 6/x-1/x/x-1

A: Known fact:

Q: 9. A zoo increased the lengths of all four sides of its rectangular monkey park by the same amount.…

A:

Q: Which equation represents the inverse, f-4), of the function f(x)= 3x+1? I+ = (x)1-f O %3D Of (a) =…

A: An inverse of a function f maps from co domain to domain with respect to the function  f. The…

Q: a.Show that 30x^3-20x^2-10 is O(x^3). b. Explain what it means for a function to be Ω(1) and give…

A: Since you have asked for a multiple question, we will solve the first question for you. If you want…

Q: Use f (x) = x – 3 and g (x) = to find the - given functions. (2 points each) 1) g • f 2) g • g Find…

A: The given functions are: f(x)=x-3          and          g(x)=xx+3

Q: Find the inverse function for /(x)32 x+5

A: Given function

Q: ∑5 (-2) ^ k -1 K=1

A: Given, ∑5-2k-1

Q: If a variable, lets say a, is >0, does that mean a goes to infinity?

A: No, this does not imply that a variable, like a, goes to infinity only because it is bigger than 0.

Q: 8. Determine the domain of f(x) = log;(x² - 2x 15) and write using interval notation.

A: Given, fx =log5x2 -2x-15 We have to find the domain  of f(x)

Q: What are the linear and exponential functions whose graphs contain the points (0,4) and (3,108)?

A: Here we have to find the linear and exponential functions whose graphs contain the points (0,4) and…

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.