Mathematics, 16.10.2019 23:30 photagraphykid

Agardener brought 5 rabbits, after 2 months rabbits became 10, and after 4 months they became 20. if the growth continues on the same ratio, what would be the amount of rabbits after 1 year?
(a) 300 (b) 435
(c) 535 (d) 635

Answers: 2

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Answer from: bm42400

The amount of rabbit after 1 year will be 320.

Step-by-step explanation:

A gardener brought 5 rabbits, after 2 months rabbits became 10.

The growth continues on the same ratio.

This represents a geometric sequence with 1st term as 5 and common ratio as 2.

As we have to find the amount of rabbit after 1 year, so the we have to find $\dfrac{12}{2}+1=6+1=7$ th term. As the time difference between each counting is 2 months, so we divided 1 year or 12 months of time by 2.

nth term in a G.P is,

$T_n = ar^{n-1}$

Putting the values,

$T_7 = 5\times (2)^{7-1}=5\times 2^6=320$

Answer from: cam3227

The amount of rabbits after 1 year is $\boxed{635}$ .

Further Explanation:

The terms of the geometric sequence can be written as,

$a,ar,a{r^2},a{r^3},..$

Here, is the first term and is the common ratio.

If the first term and the second term is known then, the value of can be obtained.

Now, the value of any term can be easily obtained with the help of a and r.

Explanation:

The initial population of the rabbit is 5.

After two months the population of the rabbit is 10.

After four months the population of the rabbit is 20.

After six months the population of the rabbit is 40.

After eight months the population of the rabbit is 80.

After ten months the population of the rabbit is 160.

After twelve months the population of the rabbit is 320.

The series can be formed as,

$5,{\text{10, 20, 40, 80, 160, 320}}$

Now find the sum of all the population.

$\begin{aligned}{\text{Sum}}&=5+10+20+40+80+160+320\\&=685\\\end{aligned}$

The amount of rabbits after 1 year is $\boxed{635}$ .

Learn more:

1. Learn more about inverse of the function .

2. Learn more about equation of circle .

3. Learn more about range and domain of the function

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Geometric progression

Keywords: Rabbit, gardener, same ratio, amount of rabbits, growth, continues, 1 year, Five rabbits, after two months.

Answer from: Quest

1200 inches = 30 yards12 inches= 1 foot3 feet= 1 yard3feet= 36 inchesyou can set up a proportion then use inverse operations that looks sorry it looks so sloppy lol

Answer from: Quest

step-by-step explanation:

6.48/4 4 goes into 6.48 1.62 times

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