Final answer:
The correct formula for determining the total population after a period of t years, with a 2% annual decline, is P(t)=45,000(0.98)ᵗ. The correct answer is option a) P(t)=45,000(0.98)ⁿ.
Step-by-step explanation:
The correct answer is option a) P(t)=45,000(0.98)ⁿ. This formula represents the total population after a period of t years, given that the population is declining at a rate of 2% each year. This is an example of an exponential decay model, where the initial population is multiplied by the base (1 - rate of decline) raised to the power of t. In this case, the rate of decline is 2% or 0.02, hence the base is 0.98. To apply this, we would use the initial population of 45,000 and raise 0.98 to the t power for each year that passes.
To determine the total population after a period of t years, we can use the formula P(t) = P0ert, where P0 is the initial population, r is the rate of change, and t is the time in years. In this case, the initial population P0 is 45,000 and the rate of change r is -2% or -0.02.
Substituting the values into the formula, we get P(t) = 45,000(0.98)t. This formula will give us the total population after a period of t years, taking into account the declining rate of 2% each year.