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Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions th

trasher [3.6K]

Answer:

(a) 100 fishes

(b) t = 10: 483 fishes

t = 20: 999 fishes

t = 30: 1168 fishes

(c)

$P(\infty) = 1200$

Step-by-step explanation:

Given

$P(t) =\frac{d}{1+ke^-{ct}}$

$d = 1200\\k = 11\\c=0.2$

Solving (a): Fishes at t = 0

This gives:

$P(0) =\frac{1200}{1+11*e^-{0.2*0}}$

$P(0) =\frac{1200}{1+11*e^-{0}}$

$P(0) =\frac{1200}{1+11*1}$

$P(0) =\frac{1200}{1+11}$

$P(0) =\frac{1200}{12}$

$P(0) = 100$

Solving (a): Fishes at t = 10, 20, 30

$t = 10$

$P(10) =\frac{1200}{1+11*e^-{0.2*10}} =\frac{1200}{1+11*e^-{2}}\\\\P(10) =\frac{1200}{1+11*0.135}=\frac{1200}{2.485}\\\\P(10) =483$

$t = 20$

$P(20) =\frac{1200}{1+11*e^-{0.2*20}} =\frac{1200}{1+11*e^-{4}}\\\\P(20) =\frac{1200}{1+11*0.0183}=\frac{1200}{1.2013}\\\\P(20) =999$

$t = 30$

$P(30) =\frac{1200}{1+11*e^-{0.2*30}} =\frac{1200}{1+11*e^-{6}}\\\\P(30) =\frac{1200}{1+11*0.00247}=\frac{1200}{1.0273}\\\\P(30) =1168$

Solving (c): $\lim_{t \to \infty} P(t)$

In (b) above.

Notice that as t increases from 10 to 20 to 30, the values of $e^{-ct}$ decreases

This implies that:

${t \to \infty} = {e^{-ct} \to 0}$

So:

The value of P(t) for large values is:

$P(\infty) = \frac{1200}{1 + 11 * 0}$

$P(\infty) = \frac{1200}{1 + 0}$

$P(\infty) = \frac{1200}{1}$

$P(\infty) = 1200$

5 0

2 years ago

A school is holding a talent show. A group of six friends entered the talent show and won the first place prize of $45, which th

Ghella [55]

Answer:

In the second group the individual members received a larger fraction of the prize money

Step-by-step explanation:

Division by Sharing

A certain amount M can be evenly split among n parties by performing a division M/n.

The first group of six friends earned $45 and they split it evenly, i.e. the same amount goes to each member. Each of them received $45/6= $7.50 apiece.

The second group of four friends won the second-place prize of $35 and they split it evenly also. Each member received $35/4=$8.75.

By comparing both numbers, we see that 8.75 is a bigger fraction of 35 that 7.50 is of 45. Each member from the second-place price will receive more money than the first group.

We can conclude in the second group the individual members received a larger fraction of the prize money

4 0

3 years ago

A bird leaves its nest and travels 20 miles per hour downwind for x x hours. On the return trip, the bird travels 4 miles per ho

marysya [2.9K]

a. if the return trip is the same then the bird traveled 40miles

b. the time of the trip is x hours + 6/x-4

Hope this helps!

5 0

2 years ago

In the past month, Kaitlin rented 1 video game and 4 DVDs. The rental price for the video game was $2.40 The rental price for ea

vichka [17]

Answer:

$2.40 for the video game and $14.8 for the DVDs

Step-by-step explanation:

1 video game = $2.40

4 DVDs = $14.8

$3.70 x 4 = $14.8

6 0

2 years ago

Write the equation of a line that is parallel to y = --x + 7 and that passes through the point (-4,1).

nordsb [41]

Answer:

slope: -1

y - 1= -(x + 4)

y - 1 = -x - 4

y = -x - 3

6 0

2 years ago

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