Explain the difference between linear, exponential, and quadratic functions in terms of their graphs, their patterns, and their rates of change.

Answers

Answer 1

Answer:

Quadratic functions are those where their rate of change changes at a constant rate. Exponential functions are those where their rate of change is proportional to itself.

An example of a quadratic function would be the shape that a ball makes when you throw it. Gravity causes a constant acceleration, the ball slows down as it is moving up, and then it speeds up as it comes down.

An example of an exponential function would be the population of a bacterium as long as there is enough space and nutrients or how your money grows with compound interest in a bank.

A quadratic function is one in the form

f(x)=ax2+bx+c  

It’s rate of change (first derivative) is linear.

f′(x)=2ax+b  

The rate of the rate of change (second derivative) is constant.

f′′(x)=2a  

Quadratics are then the solutions to the differential equation

f′′=C  

An exponential function is one in the following form.

g(x)=Aekx  

It’s rate of change is another exponential function.

g′(x)=Akekx  

So exponentials are the solutions to the differential equation

g′=kg

Step-by-step explanation:

Yes. : )


Related Questions

3x+5y=30 complete the table of values​

Answers

Answer:

O

Step-by-step explanation:

Help asap please!will mark brainliest if there's two answers

Answers

Answer:

30 square meters

Step-by-step explanation:

there is none im just saying

Given the following information about two triangles, triangle CAT and triangle DOG:

Which postulate can be used to prove triangle CAT and triangle DOG are congruent?

SSS Postulate
SAS Postulate
SSA Postulate
ASA Postulate
AAS Postulate

Choose all that apply

Answers

Answer:

1st and 3rd im pretty sure

Step-by-step explanation:

Answer:

1 and 3

Step-by-step explanation:

An expression is shown.

​ 6 n

​What is the value of the expression when n=7?

Answers

Answer:

42

Explanation:

replace n by 7 since they are equal and therefore the same thing

so 6*7=42

PLEASE JUST HELP!!!!!! Anyone!!!!

Answers

Answer:

the answer is 8 because 8 is 20% of 40

The sales data for January and February of a frozen yogurt shop are approximately normal. The mean daily sales for January was $300 with a standard deviation of $20. On the 15th of January, the shop sold $310 of yogurt. The mean daily sales for February was $320 with a standard deviation of $50. On the 15th of February, the shop sold $340 of yogurt. Which month had a higher z-score for sales on the 15th, and what is the value of that z-score

Answers

Answer:

January had a higher z-score for sales on the 15th, and the value of that z-score was of 0.5.

Step-by-step explanation:

z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

January:

The mean daily sales for January was $300 with a standard deviation of $20. On the 15th of January, the shop sold $310 of yogurt. This means, respectively, that [tex]\mu = 300, \sigma = 20, X = 310[/tex]. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{310 - 300}{20}[/tex]

[tex]Z = 0.5[/tex]

February:

The mean daily sales for February was $320 with a standard deviation of $50. On the 15th of February, the shop sold $340 of yogurt. This means, respectively, that [tex]\mu = 320, \sigma = 50, X = 340[/tex]. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{340 - 320}{50}[/tex]

[tex]Z = 0.4[/tex]

January had a higher z-score for sales on the 15th, and the value of that z-score was of 0.5.

Please help
here the question
Rosalina just started a new job. She has $500 in her bank account. Every week, she deposits $40 into her bank account.

A)
Write an expression to represent how much Rosalina has in her account at any given time using x to represent the number of weeks.
I ALREADY SOLVED A BUT I NEED HELP WITH B!!




B) Rosalina wants to save $700 for the new smart tv write and equation to determine how many weeks (x) it will take for rosalina to have enough money to purchase her new tv
HELP ME PLEASE WITH B I ALREADY SOLVED A

THANK YOU!!​

Answers

Answer:x=18

Step-by-step explanation:

if she deposites 40 every week 40 times 18 is 720 so in 18 weeks she can have a t.V

Brainliest for correct answer, any inapplicable answer or absurd answer will be deleted and reported.

Answers

Answer:

65

Step-by-step explanation:

Hi,

Triangles will always add up to 180 degrees. So, 62 + 53 = 115. Subtract it from 180, 180 - 115, and you get 65.

I hope this helps :)

Answer:

65

Step-by-step explanation:

The sum of the three angles of any triangle is equal to 180 degrees


Please help no links please help no links

Answers

Ok so the first thing you want to do is find the area of the front triangle.

14x10=140

140/2=70

So you have the area of the triangle

Now you just need to times it by 19 to get the depth

70x19=1330

Answer

1330 inches cubed

:)

What expression is equivalent to
16+2*36

Answers

Answer: It looks like this expression is 16+2 times 36, so the answer is 18 times 36 also 88, they are both equivalent

Write the slope-intercept form of the line given point and slope. ( show work if possible please)

through: (-2,-5), slope = 5 ​

Answers

Answer:

y=5x+5

Step-by-step explanation:

y-y1=m(x-x1)

y-(-5)=5(x-(-2))

y+5=5(x+2)

y=5x+10-5

y=5x+5

Pls help


Due at 5


Plsssss (NO LINKS)

Answers

Answer: if it is -7+10 then it is 3

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