A population starts at 2,500 and grows by 6% each year. Write an exponential growth model and find the population after 5 years, rounded to the nearest whole number.

Step 1: Identify the exponential growth formula.

For a quantity growing by a fixed percentage each period, use:
P(t) = P₀(1 + r)^t

where P₀ is the initial population, r is the growth rate written as a decimal, and t is the number of years.

Step 2: Identify the given values.

Initial population:
P₀ = 2500

Growth rate:
r = 6% = 0.06

Step 3: Write the growth model.

Substitute the values:
P(t) = 2500(1 + 0.06)^t

Simplify:
P(t) = 2500(1.06)^t

Step 4: Evaluate the model after 5 years.

P(5) = 2500(1.06)^5

Calculate the power:
(1.06)^5 ≈ 1.3382256

Therefore:
P(5) ≈ 2500(1.3382256)

P(5) ≈ 3345.564

Step 5: Round to the nearest whole number.

P(5) ≈ 3346

Therefore, the exponential growth model is P(t) = 2500(1.06)^t, and the population after 5 years is approximately 3,346.