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3 years ago

9

the population of a colony grows from 250 in the year 2000 to 400 in the year 2004. what is the average rate of change of popula

tion.

1 answer:

Ilia_Sergeevich [38]3 years ago

3 0

Given:

Population of a colony in 2000 = 250

Population of a colony in 2004 = 400

To find:

The average rate of change.

Solution:

Let y be the population of the colony at x year.

The population of a colony grows from 250 in the year 2000 to 400 in the year 2004. So, the two points are (2000,250) and (2004,400).

Formula for slope or average rate of change is

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m=\dfrac{400-250}{2004-2000}$

$m=\dfrac{150}{4}$

$m=37.5$

Therefore, the average rate of change of population is 37.5.

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The square root of 27 lies between which two whole numbers

Agata [3.3K]

Answer:

5 and 6

Step-by-step explanation:

The square root of 27 is 5.19615242271 , which is more than 5 but less then 6, therefore is between 5 and 6.

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3 years ago

Tony had an equal number of cranberry bars and walnut bars. He gave away 66 cranberry bars, he then had 4 times as many walnut b

Korolek [52]

Answer:

W=88

Step-by-step explanation:

4*(c-66)=c

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3 years ago

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What is the magnitude of the vector 12 - 5i?

Monica [59]

Answer:

the magnitude is 7

Step-by-step explanation:

as i means unit vector along x-axis so the magnitude of i is 1 and now,

= 12 - 5×1

= 12- 5

= 7

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3 years ago

Help please due today.

yan [13]

Answer:

I think its 2nd one

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3 years ago

Please help very urgent

Alik [6]

Answer:

32, <u>16</u>, <u>8</u>, <u>4</u>, <u>2</u>, 1

Explanation:

The geometric mean can be represented by $\sqrt[n]{x_{1} • x_{2} • x_{3} • .. x_{n}}$ .

Which is the mean of the product of n numbers, used to find the average of a geometric progression.

Don't get confused by geometric mean, it is only asking you about the next numbers in the geometric sequence given the first and sixth term.

The explicit rule for a geometric sequence can be modeled by:

$a_{n} = a_{1} • r^{n-1}$

Where $a_{n}$ is the nth term, $a_{1}$ is the first term in the sequence, n is the term number, and r is the common ratio.

Since we already know the first term, $a_{1}$ will simply be 32.

Since we know it's geometric, there will be an exponential relationship, which means that we will use the geometric mean to find the common ratio.

There are 6 total terms, r is raised to the n – 1 so 6 – 1 = 5, and that will be the degree of this root.

$\sqrt[5]{\frac{a_{6}}{a_{1}}}$ =

$\sqrt[5]{\frac{1}{32}}$ =

$\frac{1}{2}$ .

Therefore: $r = \frac{1}{2}$ .

Using all the information we have, we can find the explicit rule:

$a_{n} = a_{1} • r^{n-1}$

$a_{1}$ = 32
$r = \frac{1}{2}$

$a_{n} = a_{1} • r^{n-1}$ →

$\boxed{a_{n} = 32 • (\frac{1}{2})^{n-1}}$

________________________________

We can test that this works by substituting the number location of the term you want to find.

For instance:

$a_{1} = 32 • (\frac{1}{2})^{1-1}$

$a_{1} = 32 • (\frac{1}{2})^{0}$

$a_{1} = 32 • 1$

$a_{1} = 32$

$a_{6} = 32 • (\frac{1}{2})^{6-1}$

$a_{6} = 32 • (\frac{1}{2})^{5}$

$a_{6} = 32 • \frac{1}{32}$

$a_{6} = 1$

3 0

3 years ago

Read 2 more answers