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Anastaziya [24]

2 years ago

5

Threatened monarch butterflies are monitored by measuring the area occupied by overwintering butterflies in Mexico. According to

data collected by World Wildlife Fund Mexico, monarch butterflies occupied 1.13 hectares one recent winter, and 4.01 hectares the following winter (one year later)1. If the population is growing geometrically and grows at the same rate, how much area should the overwintering butterflies occupy one year after that

1 answer:

Pani-rosa [81]2 years ago

6 0

Answer:

14.2 hectares

Step-by-step explanation:

Fund Mexico, monarch butterflies occupied 1.13 hectares one recent winter, and 4.01 hectares the following winter (one year later)

The formula of Geometric growth

(Pt/ Po)^1/t

Where Pt = Size after t years = 4.01 hectares

Po = Initial size = 1.13

t = times = 1

=( 4.01/1.13 )^1/1

= 3.5486725664

Hence, Geometric growth rate = 3.5486725664.

It's size in hectares after another 1 year = Current size in hectares × Geometric growth rate

= 4.01 ×3.5486725664

= 14.230176991 hectares

≈ 14.2

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I tell you these facts about a mystery number, $c$: $\bullet$ $1.5 < c < 2$ $\bullet$ $c$ can be written as a fraction wit

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Answer:

Possible answer: $\displaystyle c = \frac{16}{10} = \frac{8}{5} = 1.6$ .

Step-by-step explanation:

Rewrite the bounds of $c$ as fractions:

The simplest fraction for $1.5$ is $\displaystyle \frac{3}{2}$ . Write the upper bound $2$ as a fraction with the same denominator:

$\displaystyle 2 = 2 \times 1 = 2 \times \frac{2}{2} = \frac{4}{2}$ .

Hence the range for $c$ would be:

$\displaystyle \frac{3}{2} < c < \frac{4}{2}$ .

If the denominator of $c$ is also $2$ , then the range for its numerator (call it $p$ ) would be $3 < p < 4$ . Apparently, no whole number could fit into this interval. The reason is that the interval is open, and the difference between the bounds is less than $2$ .

To solve this problem, consider scaling up the denominator. To make sure that the numerator of the bounds are still whole numbers, multiply both the numerator and the denominator by a whole number (for example, 2.)

$\displaystyle \frac{3}{2} = \frac{2 \times 3}{2 \times 2} = \frac{6}{4}$ .

$\displaystyle \frac{4}{2} = \frac{2\times 4}{2 \times 2} = \frac{8}{4}$ .

At this point, the difference between the numerators is now $2$ . That allows a number ( $7$ in this case) to fit between the bounds. However, $\displaystyle \frac{1}{c} = \frac{4}{7}$ can't be written as finite decimals.

Try multiplying the numerator and the denominator by a different number.

$\displaystyle \frac{3}{2} = \frac{3 \times 3}{3 \times 2} = \frac{9}{6}$ .

$\displaystyle \frac{4}{2} = \frac{3\times 4}{3 \times 2} = \frac{12}{6}$ .

$\displaystyle \frac{3}{2} = \frac{4 \times 3}{4 \times 2} = \frac{12}{8}$ .

$\displaystyle \frac{4}{2} = \frac{4\times 4}{4 \times 2} = \frac{16}{8}$ .

$\displaystyle \frac{3}{2} = \frac{5 \times 3}{5 \times 2} = \frac{15}{10}$ .

$\displaystyle \frac{4}{2} = \frac{5\times 4}{5 \times 2} = \frac{20}{10}$ .

It is important to note that some expressions for $c$ can be simplified. For example, $\displaystyle \frac{16}{10} = \frac{2 \times 8}{2 \times 5} = \frac{8}{5}$ because of the common factor $2$ .

Apparently $\displaystyle c = \frac{16}{10} = \frac{8}{5}$ works. $c = 1.6$ while $\displaystyle \frac{1}{c} = \frac{5}{8} = 0.625$ .

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2 years ago

Q#1:The volume of a cube is 46656 cubic metres.Find the length of each side?

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Answer:

Step-by-step explanation:

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1 year ago

Which sequence could be partially defined by the recursive formula f (n + 1) = f(n) + 2.5 for n ≥ 1?

horrorfan [7]

Option C: –10, –7.5, –5, –2.5, … is the sequence that could be partially defined by the recursive formula $f(n+1)=f(n)+2.5$

Explanation:

The given recursive formula is $f(n+1)=f(n)+2.5$ for $n\geq 1$ and $f(1)=-10$

We need to determine the sequence.

The sequence can be determined by substituting n = 1, 2, 3, 4,....

<u>2nd term of the sequence:</u>

Substituting n = 1 in the formula $f(n+1)=f(n)+2.5$ , we get,

$f(1+1)=f(1)+2.5$

Simplifying, we have,

$f(2)=-10+2.5=-7.5$

Thus, the 2nd term of the sequence is -7.5

<u>3rd term of the sequence:</u>

Substituting n = 2 in the formula $f(n+1)=f(n)+2.5$ , we get,

$f(2+1)=f(2)+2.5$

Simplifying, we have,

$f(3)=-7.5+2.5=-5$

Thus, the 3rd term of the sequence is -5

<u>4th term of the sequence:</u>

Substituting n = 3 in the formula $f(n+1)=f(n)+2.5$ , we get,

$f(3+1)=f(3)+2.5$

Simplifying, we have,

$f(4)=-5+2.5=-2.5$

Thus, the 4th term of the sequence is -2.5

Therefore, the sequence is –10, –7.5, –5, –2.5, …

Hence, Option C is the correct answer.

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2 years ago