Question

A moose population is growing exponentially following the pattern in the table shown below. Assuming that the pattern continues, what will be the population of moose after 12 years? Show all your work! Round your answer to the nearest whole number.

Answer 1

Answer:

•   7,692 moose.

Explanation:

The table that shows the pattern for this question is:

Time (year) Population

  0                   40

  1                     62

  2                    96

  3                   149

  4                   231

A growing exponentially pattern may be modeled by a function of the form P(x) = P₀(r)ˣ.

Where P₀ represents the initial population (year = 0), r represents the multiplicative growing rate, and P(x0 represents the population at the year x.

Thus you must find both P₀ and r.

1) P₀

  Using the first term of the sequence (0, 40) you get:

   P(0) = 40 = P₀ (r)⁰ = P₀ (1) = P₀

Then, P₀ = 40

 2) r

Take two consecutive terms of the sequence:

• P(0) = 40 r⁰ = 40

• P(1) = 40 r¹ = 40r = 62

• P(1) / P(0) = 40r / 40 = 62/40

• r = 62/40 = 1.55

 

You can verify that, for any other two consecutive terms you get the same result: 96/62 ≈ 149/96 ≈ 231/149 ≈ 1.55

3) Model

 

Thus, your model is P(x) = 40(1.55)ˣ

4) Population of moose after 12 years

• P(12) = 40 (1.55)¹² ≈ 7,692.019 ≈ 7,692, which is round to the nearest whole number.