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Answer:
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 [tex]\dfrac{12}{2}+1=6+1=7[/tex]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,
[tex]T_n = ar^{n-1}[/tex]
Putting the values,
[tex]T_7 = 5\times (2)^{7-1}=5\times 2^6=320[/tex]
The amount of rabbits after 1 year is [tex]\boxed{635}[/tex].
Further Explanation:
The terms of the geometric sequence can be written as,
[tex]a,ar,a{r^2},a{r^3},..[/tex]
Here, [tex]a[/tex] is the first term and [tex]d[/tex] is the common ratio.
If the first term [tex]a[/tex] and the second term [tex]ar[/tex] is known then, the value of [tex]r[/tex] 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,
[tex]5,{\text{10, 20, 40, 80, 160, 320}}[/tex]
Now find the sum of all the population.
[tex]\begin{aligned}{\text{Sum}}&=5+10+20+40+80+160+320\\&=685\\\end{aligned}[/tex]
The amount of rabbits after 1 year is [tex]\boxed{635}[/tex].
Learn more:
1. Learn more about inverse of the function https://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
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.
