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.

Time (year) Population
0 40
1 62
2 96
3 149
4 231

Answer 1

• 7,692 moose.

Step-by-step explanation:

First, you must find the pattern behind the set of data in the table shown in the question.

It is said that this is a growing exponentially pattern. Thus, the data should be modeled by a function of the form P(x) = A(B)ˣ.

And you must find both A and B.

• Finding the multiplicative rate of change (B).

B is the multiplicative rate of change of the function which is a constant that you can find by dividing consecutive terms:

• 62/40 = 1.55

• 96/62 ≈ 1.548 ≈ 1.55

• 149/96 ≈ = 1.552 ≈ 1.55

• 231/149 ≈ 1.550 ≈ 1.55

Thus, B = 1.55

• Finding the initial value A

So far, you know P(x) = A (1.55)ˣ

To find A, you can use P(0)=40, which drives to:

• 40 = A (1.55)⁰ = A(1) = A

Thus, your function is P(x) = 40(1.55)ˣ

• Finding the answer to the question

The population of moose after 12 years, is given by P(12):

• P(12) = 40 (1.55)¹² ≈ 7,692.019 ≈ 7,692

Thus, round to the nearest whole number, those are 7,692 moose.