Question

Write an explicit rule for the sequence that models this situation:

the wolf population in a local wildlife area is currently 12. due to a new conservation effort, conservationists hope the wolf population will increase by 2 each year for the next 50 years. assume the plan will be successful

Answer 1

n = 12 + 2t ,

where t is less than or equal to 50

Explanation:

Let n be the number or wolves and t be the number of years after the conservation efforts began.

n = 12 + 2t ,

where t is less than or equal to 50

Answer 2

Explanation:

The population will increase by 2 each year. This means that the sequence is an arithmetic progression.

The formula for determining the sum of n terms of an arithmetic sequence is expressed as

Sn = n/2[2a + (n - 1)d]

Where

n represents the number of terms in the arithmetic sequence.

d represents the common difference of the terms in the arithmetic sequence.

a represents the first term of the arithmetic sequence.

From the information given,

a = 12

d = 2 years

Therefore, the explicit rule for the sequence that models this situation: would be

Sn = n/2[2 × 12 + (n - 1)2]

Sn = n/2[24 + 2(n - 1)]

For the next 50 years, n = 50

S50 = 50/2[2 × 12 + (50 - 1)2]

S50 = 25[24 + 98)

S50 = 3050