Mathematics, 07.04.2020 22:28 kaylee0424

HELPP GUYSSS ::: Consider the functions:

ƒ(x) = 0.25x + 25 and g(x) = 15(1.25)x

As x approaches ∞, which statement is correct?
A) The linear function will always exceed the exponential function.
B) The exponential function will always exceed the linear function.
C) The linear function will exceed the exponential function since its initial value is greater.
D) The exponential function will exceed the linear function since its base is greater than one.

Answers: 1

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Answers

Correct option D) Base of exponential function g(x) = 15(1.25)^x is greater than 1 , this function will exceed linear function f(x) = 0.25x + 25 .

Step-by-step explanation:

Here we have , f(x) = 0.25x + 25 and g(x) = 15(1.25)x . We need to tell As x approaches ∞, which function exceeds whom! Let's find out:

f(x) = 0.25x + 25

This function is a linear function with an equation of straight line , having slope and y-intercept as :

$m=0.25\\c=25$

Graph for this function is attached below .

g(x) = 15(1.25)^x

This function is an exponential function in the form of g(x) = a(b)^x , where b>1 i.e. for rise in value of x there is exponential increase in value of y or , function .Basically Base of this exponential is greater than 1 , which makes it an increasing function ! Graph for this function is attached below .

Now , Comparing both graphs we see that as x approaches ∞ graph of exponential function g(x) = 15(1.25)^x is much more vertical than linear function f(x) = 0.25x + 25 . Since , base of exponential function is greater than 1 , this function will exceed linear function .Correct option D)

HELPP GUYSSS ::: Consider the functions: ƒ(x) = 0.25x + 25 and g(x) = 15(1.25)x As x approaches ∞, w

Answer from: Quest

solution:

as, mean is defined as sum of all the observations divided by total number of observations.

and , median is mid value of the data whether arranged in ascending order or descending order.

consider, roadsters:

2,3,4,5,6,7,8,9

mean = $\frac{2+3+4+5+6+7+8+9}{8}=\frac{44}{8}=5.5$

also, median= $\frac{5+6}{2}=\frac{11}{2}=5.5$ , because number of observations is even, so median is mean of two mid values.

now, coming to bandits

2,3,4,5,6

mean = $\frac{2+3+4+5+6}{5}=\frac{20}{5}=4$

median = 4, as number of observations is odd.

so, roadsters has greater median as well mean than bandits.

→option a is true about the repairs performed on 2 types of cars:

bandits have lower median and mean than roadsters.

Answer from: Quest

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation:

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HELPP GUYSSS ::: Consider the functions:

ƒ(x) = 0.25x + 25 and g(x) = 15(1.25)x

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