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2 years ago

What are some similarities and differences of the rates of change of linear, quadratic, and exponential functions?

Mathematics

1 answer:

gregori [183]2 years ago

5 0

Answer:

linear functions change a constant rate. i.e. the slope of the graph is constant.

d/dx (mx+b) = m

quadratic functions change at a linear rate, slower than the function itself.

The slope of the tangent to the graph is proportional to the x coordinate.

d/dx (ax^2) = 2ax

Slope of tangent to ax^2 at point (x,ax^2) is 2ax.

Exponential functions change at the same rate as the function itself. The slope of the tangent to the graph is proportional to the y coordinate.

The slope of tangent at point (x,exp(x)) is exp(x).

Definition of exp(x) is just exp(0) = 1 and d/dx exp(x) = exp(x).

d/dx exp(ax) = a exp(ax) is not part of the definition, but follows from from the chain rule

Step-by-step explanation:

You might be interested in

Which of the following expressions is equal to 3x2 + 27 ?

djverab [1.8K]

Step-by-step explanation:

The answer is provided in the options. The answer should have been A, if the question was 3x²-27.

6 0

2 years ago

The length of time for one individual to be served at a cafeteria is a random variable having an exponential distribution with a

Leya [2.2K]

Answer:

a) 0.25

b) 52.76% probability that a person waits for less than 3 minutes

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \lambda e^{-\lambda x}$

In which $\lambda = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

In this question:

$m = 4$

a. Find the value of λ.

$\lambda = \frac{1}{m} = \frac{1}{4} = 0.25$

b. What is the probability that a person waits for less than 3 minutes?

$P(X \leq 3) = 1 - e^{-0.25*3} = 0.5276$

52.76% probability that a person waits for less than 3 minutes

3 0

2 years ago

What's the domain and range for (×+4)-1

Sonja [21]

$\bf a^{-{ n}} \implies \cfrac{1}{a^{ n}}\qquad \qquad

\cfrac{1}{a^{ n}}\implies a^{-{ n}}\\
---------------\\
thus\\
(x+4)^{-1}\implies \cfrac{1}{x+4}
\\\\
$
$\bf if\qquad \cfrac{1}{0} \implies$ undefined

so.. what value of "x" makes x+4 to 0?

the domain will be, all real numbers, except that value

about the range, "y" will take, whateve "x" can provide.. in this case... I think is all real numbers, except 0, because, if you give a few big values to "x", the fraction will simply have a bigger and bigger denominator, making the fraction smaller and smaller, ever approaching 0, but never getting there

7 0

2 years ago

Sarah the cheetah ran 100 meters at a speed of 16.8 meters per second. An olympian ran the 100-meter dash in 9.6 seconds. How mu

prohojiy [21]

Answer:

Sara's speed was 6.4 meters per second faster

Step-by-step explanation:

(Were going to name the olympian steve)

First, we have to find how many meters per second Steve ran. To find this we must divide the number of meters he ran by the amount of time it took him to run all 100 meters.

100 ÷ 9.6 =10.41666667

Since the problem tells us to round to the nearest tenth of a second we round 10.41666667 to 10.4. So now we know how many meters per second Steve ran. Now all we have to do is subtract the number of meters per second Sarah ran, from the number of meters per second Steve ran.

Sarah- 16.8 meters per second

Steve- 10.4 meters per second

16.8-10.4= 6.4

And there you have it! Sarah ran 6.4 meters per second more than Steve. I hope this answer was accurate and helpful. I hope you have an AMAZING day!

6 0

3 years ago

Read 2 more answers

What is (9w)^2 (in other words, to the power of two.)

stellarik [79]

Answer:

9w to the power of is 81w

Step-by-step explanation: