Answer:
r is the common ratio (in geometric sequence)
d is the common difference (in arithmetic sequence)
n is the term number
a1 is the value of the first term
an is the value of the nth term
Step-by-step explanation:
arithmetic sequence formula:
an=a1+d(n-1)
geometric sequence formula:
an=a1•(r)^(n-1)
Answer:
Step-by-step explanation:
We have given that:
There are 20 alligators in the swamp. Each year, the number of alligators increases by 25%. There are 25 crocodiles in the swamp. Each year, 10 new crocodiles join the swamp
Part A:
According to the above mentioned statement the function for representing the number of alligators and crocodiles in the swap throughout the year is:
Alligators = y=20(1.25)^x (x represents years)
crocodiles: y=10x+25
Part B:
Number of alligators after 4 years in the swap = y=20(1.25)^x
Number of alligators after 4 years in the swap = y=20(1.25)^4
Number of alligators after 4 years in the swap=48.82
This shows that about 48 to 49 alligators will be there in the swap after 4 year
Number of crocodiles after 4 years in the swap = y= 10(4)+25 = 65
Part C:
We will use the graph method to solve this part:
After approximately 7 years, the number of animals of each type will be the same, 95.
X increases by one
y increases by 2
(5, 1) - > (x + 1, y + 2) -> (6, 3)