In 2011, the population of deer in a forest was 650.

1. In 2012, the population increases by 15%. Write an expression, using only multiplication, that represents the deer population in 2012.
2. In 2013, the population increases again by 15%. Write an expression that represents the deer population in 2013.
3. If the deer population continues to increase by 15% each year, write an expression that represents the deer population years after 2011.

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".

Answer:

Graph 1- last option choice

Graph 2- first option choice

Graph 3- third option choice

Graph 4- second option choice

Hope this helps stay safe!

Step-by-step explanation:

When graphing a linear inequality on a number line, use an open circle for "less than" or "greater than", and a closed circle for "less than or equal to" or "greater than or equal to".

Answer:

1. x < 1

2. x </= 1

3. x >/= - 1

4. x > 1

Answer:

105.978947368

Step-by-step explanation:

He would pay $14.48

To get this answer you would need to multiply $2.73 by 24 and subtract by $80.

Answer:

Not a function because an output has two different inputs

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

the first number in slope intercept is the slope and the second number is the y-intercept

Answer:

The answer is Choice a

Step-by-step explanation:

Hey there!

I think the answer is B.

Answer:

9 months

Step-by-step explanation:

651=58x+129

-129         -129

522=58x  divide 522 by 58

=9

Answer:

y = 9

Step-by-step explanation:

y-y1 = m(x-x1)

m is the slope =y2-y1/x2-x1=9-9/-2-3=0

pick any number out of the given two for (x1, x2)

y-9 = 0*(x-3) so

y-9 = 0 add 9 to both sides

y = 9

solution

X + k

X - 2k

=X+k-x-2k

=x-x+k-x-2k

=0-k

=-k

or,

1

k

Answer:

Step-by-step explanation: 56

Answer:

130 is correct

Step-by-step explanation:

Answer:

-2.4f - 21

Step-by-step explanation:

Answer:

4x ≤ 30

Step-by-step explanation:

Omar gets 30 dollars off because $25 + $5 = 30. Let x = pairs of socks

We know each pair costs $4, so the cost would be 4x. Omar has to buy as many pairs as he can with only the coupon and gift card. Omar has to spend $30 (the full discount) or less than $30. Therefore, the inequality would be: 4x ≤ 30 or 4x is less than or equal to 30 ($30).

Answer: 4p-5_<25

Step-by-step explanation:

i got i right

Answer:

Thus, a product that normally costs $55 with a 40 percent discount will cost you $33.00, and you saved $22.00. You can also calculate how much you save by simply moving the period in 40.00 percent two spaces to the left, and then multiply the result by $55 as follows: $55 x . 40 = $22.00 savings.

Step-by-step explanation:

Answer:

[tex](3^6)^{18}=3^{108}=3.38139191\times10^{51}[/tex]

Answer:

C

Step-by-step explanation:

Each x value only corresponds with 1 y value

Answer:

Audrey was charged $3 for each withdrawal.

Step-by-step explanation:

We have to calculate the amount of money charged on one transaction.

In order to find the amount for one ATM withdrawal, the total amount for ATM withdrawals will be divided by number of withdrawals.

Given

[tex]Total\ ATM\ withdrawal\ fees = \$51\\Total\ withdrawals = 17\\Amount\ for\ one\ withdrawal = \frac{Total\ fees}{No.\ of\ withdrawals}\\= \frac{51}{17}\\= \$3[/tex]

Hence,

Audrey was charged $3 for each withdrawal.

Answer:

use a calculator that should help u so much

Answer:

oof this is easy

Step-by-step explanation:

Straight angles consists with

two right angles

2

Straight angles consists with

one obtuse angle and one acute angle

RESULT

My friend is wrong because a straight angle either consists with two right angles or one obtuse angle and one acute angle.

Answer:

0-^

Step-by-step explanation:

Answer:

m= 120 - 6*d

Step-by-step explanation:

budget is $120 per 1 month, spends $6 per 1 day

on the the table you have 2 columns: one labele it "days" and one "$ spent" and fill it in:  

days: 1,2,3,4,..

$ spent: 6, 6*2=12, 6*3= 18, 6*4= 32,...

on the graph lable the horizontal axis "days" and the vertical axis "$ spent"

now plot the points (1,6), (2,12),(3,18), ..., and draw a line trough them

the equation is

m= 120 - 6*d

so after 20 days for example, out of 120 will have m=120-6*20=120-120=0,

$0 wil have in 20 days

Answer: 32

2+6(6-2)

8(4)

32

Answer: (0,0),(0,4), and (5,0)

Step-by-step explanation:

It is easy to find lengths of horizontal and vertical segments and distances from (0,0) so always place one vertex at the origin and one or more sides on an axis.

This answer has an x intercept and y intercept.

Answer:

20.47.

Step-by-step explanation:

You need to 56.34, by 35.87. And you get your answer. 20.47!

Answer:

Altitudes in a triangle

option 2

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

The inverse of [tex]\displaystyle{f(x)=4x^3+8}[/tex] is determined to be [tex]{f^{-1}(x)=\sqrt[3]{\frac{1}{4}x-8}[/tex].

Step-by-step explanation:

In order to find the inverse of a function, we need to know a couple of rules about functions.

Following these rules, our function now becomes [tex]\displaystyle{x=4y^3+8}[/tex].

We now can simplify it further in order to find the value of x.

[tex]\displaystyle{x=4y^3+8}\\\\4y^3=x-8\\\\y^3=\frac{x}{4}-8\\\\\sqrt[3]{y^3}=\sqrt[3]{\frac{x}{4}-8} \\\\y = \sqrt[3]{\frac{1}{4}x-8}\\\\f^{-1}(x)= \sqrt[3]{\frac{1}{4}x-8}[/tex]

Therefore, the inverse of [tex]\displaystyle{f(x)=4x^3+8}[/tex] is [tex]\displaystyle{f^{-1}(x)=\sqrt[3]{\frac{1}{4}x-8}[/tex].

Answer:

[tex]\huge\boxed{f^{-1}(x) = \sqrt[3]{\frac{x-8}{4}}}[/tex]

Step-by-step explanation:

In order to find the inverse of a function, we need to follow a series of steps.

1. Write the function in the form [tex]y=ax^b+c[/tex]

2. Swap where the x and y values are

3. Solve for y

4. Convert into [tex]f^{-1}(x)[/tex] form

So first, we can write [tex]f(x)=4x^3+8[/tex] as [tex]y=4x^3+8[/tex].

Now we need to swap where the x and y variables are. This makes our equation [tex]x=4y^3+8[/tex].

To find the inverse, we now need to solve for y in this equation.

Therefore, the inverse of this function is [tex]f^{-1}(x) = \sqrt[3]{\frac{x-8}{4}}[/tex].

Hope this helped!

Answer:

3 shoes

Step-by-step explanation:

You can set up an equation to solve this question like this:

200=45s+26

174=45s

174/45=s

s=3.867

You can't have a part of a shoe, so you have to round down to get 3 shoes

Answer:

3

Step-by-step explanation:

In order to get the answer to this question you subtract in till you can no longer subtract after subtracting the cost of the bag.

What we do know:

[tex]M=200[/tex]

[tex]B=26[/tex]

[tex]S=45[/tex]

[tex]200-26=174[/tex]

[tex]174-45=129[/tex]

[tex]129-45=84[/tex]

[tex]84-45=39[/tex]

[tex]S=3[/tex]

Hope this helps