I need number 23 QUICK!

The equation y=6.72(1.014) x models the world population y , in billions of people, x years after the year 2000 . Find the year

Marizza181 [45]

the population will reach 8 billion by 2012 ,as calculated by properties of logarithm.

<h3>What is Logarithm?</h3>

The opposite of exponentiation is the logarithm.
This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.
A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.

Given:

y = 6.72 ( $1.014^x$ ), where

y = population in billions
x = time in years

To find: Year when population is 8 billion, i.e., y = 8.

Finding:

8 = 6.72 ( $1.014^x$ )

=> $\frac{8}{6.72}= ( 1.014^x)$

Taking log on both sides

=> $log(\frac{8}{6.72})= log( 1.014^x)$

=> log(1.19) = x (log 1.014) (as $log_b(a)^m = m (log_b(a))$ )

=> $\frac{log(1.19)}{log (1.014)}$ = x

=> x = $\frac{0.0755}{0.006}$

=> x = 12.58

Hence, the population will reach 8 billion by 2012 ,as calculated by properties of logarithm.

To learn more about logarithms, refer to the link: brainly.com/question/25710806

#SPJ4

5 0

1 year ago

Given that 3^x = 4^y = 12^z, show that z = (xy)/(x+y).

irinina [24]

$3^{x} = 4^{y} = 12^{z}$
$3^{x} = 4^{y} = (4 \cdot 3)^{z}$
$3^{x} = 4^{y} = 4^{z} \cdot 3^{z}$

$\text{Let a } = 3^{x} = 4^{y} = 4^{z} \cdot 3^{z}$
$log_3a = x$
$log_4a = y$
$log_{(4 \cdot 3)}a = z$

Using change of base:
$x = \frac{lna}{ln3}$
$y = \frac{lna}{ln4}$
$z = \frac{lna}{ln(4 \cdot 3)}$

$ln3 = \frac{lna}{x}$
$ln4 = \frac{lna}{y}$
$ln(4 \cdot 3) = \frac{lna}{z}$

Now, ln(4 · 3) = ln(4) + ln(3)

$\frac{lna}{z} = \frac{lna}{x} + \frac{lna}{y}$
$\frac{1}{z} = \frac{1}{x} + \frac{1}{y}$
$\frac{1}{z} = \frac{x + y}{xy}$

$\therefore z = \frac{xy}{x + y}$

8 0

4 years ago

Which point is located at 5_2

alexdok [17]

Hey there!

Point D is located at point (5, -2)

In coordinates, the first number represents the x-coordinate, and the second number represents the y-coordinate. (TIP: YOU MUST START AT THE ORIGIN, OR (0, 0). In the x-coordinate, you go left/right that number of spaces, left for negative and right for positive. For the y-coordinate, you go up/down that number of spaces, down for negative and up for positive. This means that the point (5, -2) is 5 units right and 2 units down, which lands on point D.

Hope it helps and have an amazing day!

4 0

3 years ago

Solve <br> -3.1 - 2.5 and explain for 100 points<br> HURRY I NEED THE ANWSER TODAY

lilavasa [31]

Answer: -5.6

Step-by-step explanation:

-(3.1+2.5)= -5.6

7 0

3 years ago

Find the product of 14,560 x10

ad-work [718]

145600.. . .. ...........

3 0

3 years ago