An internet analytics company measured the number of people watching a video posted on a social media platform. The company found 129 people had watched the video and that the number of people who had watched it was increasing by 30% every 3 hours.
(a)
Write an exponential function for the number of people A who had watched the video n hours after the initial observation. (Enter a mathematical expression.)

Answer:

(a) The exponential function representing the number of people who had watched the video [tex]t[/tex] hours after the initial observation is [tex]n(t) = 129\cdot 1.3^{\frac{t}{3} }[/tex].

(b) As [tex]n(120) < 5\times 10^{6}[/tex], we conclude that this video is not going "viral".

Step-by-step explanation:

Statement is incomplete. The complete statement is:

An internet analytics company measured the number of people watching a video posted on a social media platform. The company found 129 people had watched the video and that the number of people who had watched it was increasing by 30% every 3 hours.

(a) Write an exponential function for the number of people A who had watched the video n hours after the initial observation.

(b) A video is said to go "viral" if the number of people who have watched the video exceeds 5 million within 5 days (120 hours). Would this video be considered to have gone viral?

(a) From the statement of the problem we get the following relationship:

[tex]\frac{n_{i+1}}{n_{i}}= r^{[(i+1)-i]}[/tex] (Eq. 1)

Where:

[tex]n_{i}[/tex] - i-th number of people watching a video, dimensionless.

[tex]n_{i+1}[/tex] - (i+1)-th number of people watching a video, dimensionless.

[tex]r[/tex] - Increase ratio, dimensionless.

For Induction Theorem, we get the following relatioship for [tex]i = 0[/tex]:

[tex]\frac{n_{1}}{n_{o}} = r^{1-0}[/tex] (Eq. 2)

For [tex]i = m[/tex], the following relationship is constructed:

[tex]\left(\frac{n_{1}}{n_{o}} \right)\cdot \left(\frac{n_{2}}{n_{1}} \right)\cdot ...\cdot \left(\frac{n_{m+1}}{n_{m}} \right) = r^{m}[/tex]

[tex]\frac{n_{m+1}}{n_{o}} = r^{m}[/tex](Eq. 3)

And for [tex]i = m+1[/tex], we have the following expression:

[tex]\left(\frac{n_{1}}{n_{0}} \right)\cdot \left(\frac{n_{2}}{n_{1}} \right)\cdot ...\cdot \left(\frac{n_{m+2}}{n_{m}} \right) = r^{m+1}[/tex]

[tex]\frac{n_{m+2}}{n_{0}} = r^{m+1}[/tex](Eq. 4)

If we multiply (Eq. 3) by the (m+1)-th ratio based on (Eq. 1):

[tex]\left(\frac{n_{m+1}}{n_{o}}\right)\cdot \left(\frac{n_{m+2}}{n_{m+1}} \right) = r^{m} \cdot r[/tex]

[tex]\frac{n_{m+2}}{n_{o}} = r^{m+1}[/tex]

Which is (Eq. 4) and the exponential function is represented by:

[tex]n_{i+1} = n_{o}\cdot r^{i}[/tex], [tex]i\in \mathbb{N}_{O}[/tex] (Eq. 5)

As the number of people is increased at constant rate every 3 hours, we get that [tex]i[/tex] is:

[tex]i = \frac{t}{3}[/tex], [tex]t \in \mathbb{R}[/tex], [tex]t \geq 0[/tex] (Eq. 6)

Where [tex]t[/tex] is the time, measured in hours.

Then, the exponential function is:

[tex]n(t) = n_{o}\cdot r^{\frac{t}{3} }[/tex] (Eq. 7)

Where [tex]n_{o}[/tex] is the initial number of people watching the video, dimensionless.

If we know that [tex]n_{o} = 129[/tex] and [tex]r = 1.3[/tex], then the exponential function representing the number of people who had watched the video [tex]t[/tex] hours after the initial observation is:

[tex]n(t) = 129\cdot 1.3^{\frac{t}{3} }[/tex]

(b) If we know that [tex]t = 120\,h[/tex], then we evaluate the exponential function:

[tex]n (120) = 129\cdot 1.3^{\frac{120}{3} }[/tex]

[tex]n(120) = 4.659\times 10^{6}[/tex]

As [tex]n(120) < 5\times 10^{6}[/tex], we conclude that this video is not going "viral".

(0.1296)^3/4 of law of indices plz step by step​

can anyone help me please?

What is the solution to this system 2x + y = 1 3x – y = –6 (–1, 3)

Find the common difference of the sequence shown.
1/6, 1/3, 1/2, 2/3...
-1/12
-1/6
-1/3

9-(7-3x) = 4+x-(3-x) solve for x

The Hu family goes out for lunch, and the price of the meal is $53. The sales tax on the meal is 7%, and the family also leaves a 15% tip on the pre-tax amount. What is the total cost of the meal?

The total cost of the meal is $

Please help!! Solve for x

The ratio of boys to girls in a class is 3:4. There are 35 students in the class. How many students are boys?

Ms. Cruz has a tank with 11 fish. After buying two more, she has 2 less than triple the amount of fish Ms. Montesinos has. How many fish does Ms. Montesinos have in her tank?

a) Write a let statement below to define your variable(s):

b) Set up an equation using the variable you defined in (a):

c) Solve your equation & Check. How many fish does Ms. Montesinos have? JUST TYPE THE NUMBER. EXAMPLE: IF SHE HAS 17 FISH JUST TYPE "17"

d) Upload a picture of your SOLUTION & CHECK.

plzz help mee

Need help. (please look at the image file)

∆GHI is an isosceles triangle with a vertex angle H If the m∠H=80°, then find the m∠I.

Four friends race their bikes down the street.
Evan finishes in 6.2 seconds, Devon in 6.0999 seconds, Liza in 6.188 seconds, and Tasha in 6.168 seconds.
Which order shows the friends’ times from fastest to slowest?
A.

Tasha, Liza, Evan, Devon

PLZZ HELPP I HAVE TO GO SOMEWHERE RN ASAP! (:
Which statement is true about the theory of plate tectonics and the theory of continental drift?

A. The theory of plate tectonics explains how continental movements could occur.

B. The theory of plate tectonics tells exactly where the continents were before Pangaea divided.

C. The theory of plate tectonics shows that continental movements could not have happened.

D. The theory of plate tectonics shows that Pangaea was impossible, but the continents did move.

¿Cuál es la frecuencia absoluta de 2 puntos?
2-3-2-3-4-1-4-3-3-2

Triangles A B C and L M N are shown. Angle B A C is 58 degrees. Angle M L N is 78 degrees. Sides A B and L M are congruent. Sides A C and L N are congruent.
Given AC = LN and BA = ML, which statement must be true?
BC < MN
BC > MN
BC = MN
BA = LN

Which equation represents a line which is parallel to x = 0?
helppp pleaseee

-7(-1+7k)-3(8k-1)
What the answer?

suatu kelas yang berjumlah 25 siswa,terdapat 20 siswa yg senang sepak bola, 15 siswa senang bulutangkis dan 3 siswa tidak senang keduanya. banyaknya siswa yg senang keduanya adalah?

Consider the inequality -20.2 > 0y. Which of the following must be true?
Check all that apply.
____________________________________________________________
A) You cannot divide by zero.

B) The inequality is equivalent to -20.2 > 0, which is false.

C) The solution is y > 0.

D) The solution is 0 > y.

E) The solution is y = 0.
____________________________________________________________

NEED RN, WORTH 30! ~ please and thank you! <3

the first photo is number one, and the second photo is number two :)

1) Noah ate all of his Takis for breakfast, but he forgot that he owed Jason 16
Takis. London gave Noah 27 Takis at lunch the next day. How many Takis
will Noah have in total after he give Jason the Takis?

Help on this please

I don't know how you got that answer.
you must be very clever lol.
The answer is actually x=3cm

ten Susan works at the local ice cream shop with her friend Tara. Susan is a shift supervisor and is paid $9.50 an hour. The owner of the shop decided to give Susan a bonus of $25 in her upcoming check to say thanks for all of her hard work. Which function shows Susan's salary (S), if she works h hours during the upcoming week?

1. S(h) = 9.50h + 25
2 S(h) = 9.50h - 25
3. S(h) = 25h + 9.25
4. S(h) = 9.50 + 25​

HELP PLEASE ! ASAP !

can you guys solve this please a movie theaters has 4 groups of seats the largest group of seats in the middle has 20 rows with 20 in each row there are 2 smaller groups of rows of seats on the sides each row a group of seats in the back has 5 rows with 30 rows of seats in each row how many seats are in the movie theaters

The sums of _____ integers can be either positive or negative.

what is X for this 2x+7-6x=23

Need help on Homework​

The points in the table lie on a line. Find the slope of the line.