What is the equation relating x and

PLZ HELP THIS IS TIMED!!!!

mihalych1998 [28]

Answer:

For the sequence is $-\frac{2}{3}$ ,-4 ,-24 ,-144 ,...

Hence the formula $f(x)=-\frac{2}{3}(6)^{x-1}$ for x=1,2,3,... represents the given geometric sequence

Step-by-step explanation:

Given sequence is $-\frac{2}{3}$ ,-4 ,-24 ,-144 ,...

To find the formula to describe the given sequence :

Let $a_1=\frac{-2}{3}$ , $a_2=-4$ , $a_3=-24$ ,...

First find the common ratio

$r=\frac{a_2}{a_1}$ here $a_1=\frac{-2}{3}$ and, $a_2=-4$

$=\frac{-4}{\frac{-2}{3}}$

$=\frac{4\times 3}{2}$

$=\frac{12}{2}$

$r=6$

$r=\frac{a_3}{a_2}$ here $a_2=-4$ and $a_3=-24$

$=\frac{-24}{-4}$

$=6$

$r=6$

Therefore the common ratio is 6

Therefore the given sequence is geometric sequence

The nth term of the geometric sequence is

$a_n=a_1r^{n-1}$

The formula which describes the given geometric sequence is

$f(x)=a_1r^{x-1}$ for x=1,2,3,...

$=\frac{-2}{3}6^{x-1}$ for x=1,2,3,...

Now verify that $f(x)=a_1r^{x-1}$ for x=1,2,3,... represents the given geometric sequence or not

put x=1 and the value of $a_1$ in $f(x)=a_1r^{x-1}$ for x=1,2,3,...

we get $f(1)=-\frac{2}{3}(6)^{1-1}$

$=-\frac{2}{3}(6)^0$

$=-\frac{2}{3}$

Therefore $f(1)=-\frac{2}{3}$

put x=2 we get $f(2)=-\frac{2}{3}(6)^{2-1}$

$=-\frac{2}{3}(6)^1$

$=-\frac{12}{3}$

Therefore $f(2)=-4$

put x=3 we get $f(3)=-\frac{2}{3}(6)^{3-1}$

$=-\frac{2}{3}(6)^2$

$=-\frac{2(36)}{3}$

Therefore $f(3)=-24$

Therefore the sequence is f(1),f(2),f(3),...

Therefore the sequence is $-\frac{2}{3}$ ,-4 ,-24 ,-144 ,...

Hence the formula $f(x)=a_1r^{x-1}$ for x=1,2,3,... represents the given geometric sequence is verified

Therefore the formula $f(x)=-\frac{2}{3}(6)^{x-1}$ for x=1,2,3,... represents the given geometric sequence

7 0

3 years ago

Read 2 more answers

Minnie organizes data in a table to show the net change in the number of people subscribing and unsubscribing to her blog each m

olchik [2.2K]

The factored expression which represents the net change in the number of blog subscriptions over 10 months is :

3(11 - 7) + 4(-8)
Hence, the net change is -20

Change : -8, 11, -7, -7, -7, -8, -8, -8, 11, 11

To factor the values in the change variable :

-7 has a frequency of 3

-8 has a frequency of 4

11 has a frequency of 3

Values having the same frequency can be factored together :

Hence, we have ;

3(11 - 7) = 3(11 - 7) = 3(4) = 12 - - - - (1)

-8 having a value of 4 can be factored thus ; 4(-8) = -32 - - (2)

Joining both equations :

3(11-7) + 4(-8)

3(11 - 7) + 4(-8)

3(4) + 4(-8)

12 + (-32)

= - 20

Therefore, the factored expression for the net change in subscription is 3(11-7) + 4(-8)

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8 0

2 years ago

A car depreciated $2000 each year it was owned and driven. What type of depreciation is this?

Greeley [361]

Straight line depreciation, the value of the car is given by the following equation, where V is the value of the car, and O is the original value of the car, and x is the number of years since buying the car. V=O-2x This equation follows the form of a straight line, that is: y=mx+b

3 0

3 years ago

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The sum of two numbers is 100, the difference between the two numbers is 26. What is the number that is less?

Zepler [3.9K]

The numbers that would be smaller would be the two with the difference of 26.
27-1=26 where as, if you were to use a 1 in each, 99+1= 100. Therefore 27 and 1 (28) is less than 99 and 1 (100).

6 0

4 years ago

List the transformations of the function<br> j(x) = 3(-7(x+2))-4

allsm [11]

Answer:

transformations of function 3(-7(x+2))-4

vertical stretch
horizontal compression
translates left
translates down
reflection across y-axis

8 0

3 years ago