Suppose the number of Twitter followers for a particular celebrity x months afte opening her account can be modeled by the function below. f(x) = -20,000x² + 800,000x %3D Use this equation to determine the average rate of increase, in followers during her first year on Twitter. per month. Answer = followers per month

Q: 3. Write the equation of the function graphed below. S(x) = 1,

A: The solution of the given problem is given below. Which is easily infered from the graph.

Q: The height of a projectile fired vertically into the air (neglecting air resistance) at an initial…

A: The height of projectile f(x) in feet is given by f(x)=96x-16x2, where x is time in seconds. The…

Q: The growth of a certain bacteria can be modelled by the function, f(x)=250e^ .06t4t , where t is the…

A:

Q: Find the slope of the graph of the function at the given point. f(x) = 4(9 − x)2;    (9, 0)

A: Given,  The function is f(x) = 4(9 − x)2;    (9, 0).

Q: Using U.S. Census Bureau projections from 2020 to 2060, the number of U.S. females under the age of…

A: Answer

Q: Find the slope of f(x) = -2x² + 2x + 3 at (2, – 1). Use a graphing utility and round to the nearest…

A: Consider the provided function and the point, fx=-2x2+2x+3   at 2,-1 Find the slope of the function.…

Q: A company estimates the profit for selling a certain commodity by the given function, P(x) = -x2…

A: We will find out the required value.

Q: Find the slope of the graph of the function at the given point.

A: We have the given function as fx=27x3            ⋯⋯1 In order to find the slope of the given…

Q: The number of images on a computer screen grows according to the function f(x) = 700(3*), where x is…

A:

Q: Order the functions from slowest growing to fastest growing as x -o: 4x², (In x)³, 10*, and e2x

A:

Q: The value, V, of a computer can be modeled by the function y) = 1, 300(61)', where t is the number…

A: Given that V represents the value of a computer and t represents the number of years since the…

Q: The number of Instagram monthly active users (in millions) between 2013 and 2015 can be modeled…

A: The number of instagram monthly active users between 2013 and 2015 be the…

Q: On a recent scuba diving trip, Kate and Kara reached a depth of 130 feet. Six-and-a-half minutes…

A:

Q: Find the point of diminishing returns for the function, where R is the revenue (in thousands of…

A:

Q: The percentage of gross domestic product​ (GDP) in a state going toward health care from 2007…

A: Given, the modelled function f(x) = 1.3lnx + 14.7, where f(x) is the percentage of gross domestic…

Q: In the piecewise function in the picture, what does y equal when x=3?

A:

Q: Find the slope of the graph of the function at the given point.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Determine where the graph of the function f (x) = x³ – 6x² is concave upward and concave downward.

A:

Q: Find the slope of the graph of the function at a given value. f(x) = -3x2 + 8x - 6/x2 when x = 5.

A:

Q: Which equation matches the graph of the piecewise function f(x) below?

A: Given,

Q: A group of 6 students is surveying their classmates to get feedback about the different clubs…

A:

Q: Write the function defined by y=f(x),subject to the condition of the value of f(x) is 16 times the…

A: The function defined by y=fx , subject , to the condition of thevalue of fx is 16 times the value…

Q: The aerobic rating of a person x years old is modelled by the function A(x) = 110(In x-2) for x 2…

A: The maxima and minima can be found for the function by differentiation. For the values of maxima the…

Q: Use the graph of the function to find its average rate of change from x = -9 to x -5. Simplify your…

A: average rate of change be "R"points x=-9 , x=-5Rate of change is gevn by R=f(b)-f(a)b-aat x=-9 ,…

Q: In the given equation , sketch the graph of the function   y = 3- lxl

A: A function is a relation which maps each element in its domain to exactly one value in its range.…

Q: The average price for a movie ticket in Detroit, Michigan was $8 in 2010, and it increases at 7% per…

A: To Determine: The average price for a movie ticket in Detroit, Michigan was $8 in 2010, and it…

Q: Find the slope of the graph of the function at the given point. 256 f(x) = (4, 1) f'(4) =

A: Explained below

Q: Find the slope of the graph of the function at the given value. f(x)= 2x² + 4 when x = 5

A: Slope of graph of function at given point is first derivative of function at that point.

Q: Graph the function. ​f(x)=−5x

A: The given function is f(x)=-5x

Q: A store charges 1.50 for a 20-oz bottle of sport drink. Which equation best represents the total…

A:

Q: Graph the following equations and explain why they are not graphsof functions of x. y2 = x2

A:

Q: In 1990, the population of Bend, Oregon was 722. In 2000, the population had grown to 977.  Using…

A: Let us denote t= years after 1990  So, 1990 means t=0 and 2000 means t=2000-1990=10 So the…

Q: While riding his bicycle, a rock becomes embedded in Joshua's tire. The equation roprosenting the…

A:

Q: Write the equation of the parent function f(x) = x3 after it has been translated five units left,…

A: Given function We need to determine the function after f(x) has been translated 5 units left,…

Q: Find the slope of the graph of the function at the given value. f(x) = 4x+ 8. when x = 5 %3D

A:

Q: downtown parking lot charges 5 per hour for the first 2 hours, then 2.50 per hour after that. Which…

A: A downtown parking lot charges 5 per hour for the first 2 hours, then 2.50 per hour after that. To…

Q: the number x (in thousands) of cat flea collars demanded each year when the price of a collar is p…

A:

Q: A paper airplane was thrown from the top of a 9 meter tall house and falls at a rate of 3 meters…

A: Given  The height of the paper airplane above the ground can be found using  the function  y  =…

Q: A 12-inch tall sunflower is planted in a garden and the height of the sunflower increases by 8% per…

A: As per our guidelines, we are allowed to answer first three sub-parts only. Thanks A 12-inch tall…

Q: Find the points on the graph of the function that are closest to the given point. f(x) = x2 - 8, (0,…

A:

Q: The total yield of corn on Mr. Geller's farm from 1991 to 2010 can be modeled by the function f(x)…

A:

Q: The size of the raccoon population in a park increases  at 4.9%, with a current population at 119,…

A: To find the population of raccoons in 6 years.

Q: The function  models the daily profit, f(x)=-x2 +46x-360, in hundreds of dollars, for a company that…

A: f(x) = -x 2 + 46 x - 360 f(x) represents the daily profit in hundred so f(x) = 88

Q: the height of a ball Doreen tossed into the air can be modeled by the function h(x) =…

A:

Q: Determine where the given function is increasing and where it is decreasing  45x3  -3x5

A: A function is increasing if f'(x) > 0 and decreasing if f'(x) < 0.

Q: The length of a rectangle is 3 inches more than the width. Which of the following represents the…

A:

Q: The number of cats in Eugene is increasing at a constant rate. Four weeks ago, the number of cats…

A: (a) Consider the increase in number of cats in four weeks is, 50000-48000=2000 Then, the rate of…

Q: flx)=メー6x+ 2x +8

A:

Q: Suppose a gift basket maker incurs costs for a basket according to C(x)=18x+220. If the baskets are…

A: Given  C(x)=18x+220 The baskets are sold for $43 per basket.

Q: The graph of f(x)=x^2 rises or falls to the left? And does it rise or fall to the right?

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.