2. Select all ratios that are equivalent to 3:18. 21:126 6:36 1:6 1:18 15 21

In 1859, 24 rabbits were released into the wild in Australia, where they had no natural predators. Their population grew exponen

Mashcka [7]

Answer:

a) P' = P

$P(t) = 24e^{0.693t}$ where t is step of 6 months

b) 7.7 years

c)1064.67 rabbits/year

Step-by-step explanation:

The differential equation describing the population growth is

$\frac{dP}{dt} = P$

Where t is the range of 6 months, or half of a year.

P(t) would have the form of

$P(t) = P_0e^{kt}$

where $P_0 = 24$ is the initial population

After 6 month (t = 1), the population is doubled to 48

$P(1) = 24e^k = 48$

$e^k = 2$

$k = ln(2) = 0.693$

Therefore $P(t) = 24e^{0.693t}$

where t is step of 6 months

b. We can solve for t to get how long it takes to get to a population of 1,000,000:

$24e^{0.693t} = 1000000$

$e^{0.693t} = 1000000 / 24 = 41667$

$0.693t = ln(41667) = 10.64$

$t = 10.64 / 0.693 = 15.35$

So it would take 15.35 * 0.5 = 7.7 years to reach 1000000

c. $P' = P_0ke^{kt}$

We need to resolve for k if t is in the range of 1 year. In half of a year (t = 0.5), the population is 48

$24e^{0.5k) = 48$

$0.5k = ln2 = 0.693$

$k = 1.386$

Therefore, $P' = 1.386*24e^{1.386t}$

At the mid of the 3rd year, where t = 2.5, we can calculate P'

$P' = 1.386*24e^{1.386*2.5} = 1064.67$ rabbits/year

4 0

3 years ago

I need help!! I don’t know which one it is. Which point is closest to point A? Point__

aleksandrvk [35]

Answer:

Point D

Step-by-step explanation:

The length from Point A to Point D is 6 units, while the length from point A to Point C is 7 units, and the length from Point A to Point B is also 7 units. Because to reach Point C, you have to make one turn, adding one more unit. Same with Point B.

4 0

2 years ago

Read 2 more answers

i need help with the last two. I forgot the formula and wondering if you will help me find which one is and isnt a triangle

Nimfa-mama [501]

Answer:

3. D) 26, 7, 31

4. B) 6, 34, 27

Step-by-step explanation:

Both #3 and #4 use the same strategy: the two shorter sides' sum has to be greater than the longer side.

#3:

2 + 8 is 10, which is less than 13. So A wouldn't form a triangle.

12 + 22 is 34, which is the length of the longer side. So B wouldn't form a triangle either.

14 + 18 is 32, which is less than 40. So C wouldn't form a triangle.

7 + 26 is 33, which is greater than 31. So D would form a triangle.

D. 26, 7, and 31 are the only lengths of the ones shown that form a triangle.

#4:

17 + 18 is 35, which is greater than 19. So A would form a triangle.

11 + 22 is 33, which is greater than 25. So C would also form a triangle.

5 + 18 is 23, which is greater than 20. So D would form a triangle.

6 + 27 is 33, which is less than 34. So B wouldn't form a triangle.

B. 6, 34, and 27 are the only lengths of the ones shown that don't form a triangle.

6 0

3 years ago

HELP MEEEE How do you add and subtract functions?

nata0808 [166]

Answer:

To add or subtract functions, just add or subtract the values at each point where it makes sense. If the functions are given by formulas, you can just add or subtract the formulas (it doesn't matter whether you plug in values before or after).

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Find four consecutive integers with a sum of 106.

grandymaker [24]

4 consecutive integers...
x, x + 1, x + 2, x + 3

x + x + 1 + x + 2 + x + 3 = 106
4x + 6 = 106
4x = 106 - 6
4x = 100
x = 100/4
x = 25

x + 1 = 25 + 1 = 26
x + 2 = 25 + 2 = 27
x + 3 = 25 + 3 = 28

ur 4 integers are : 25,26,27,28

6 0

3 years ago