Question

5 mark for review a model predicts that the population of bergen was 15,000 in 2005. the model also predicts that each year for the next 5 years, the population p increased by 4% of the previous year’s population. which equation best represents this model, where x is the number of years after 2005, for x ≤ 5? a p = 0.96(15,000)^x b p = 1.04(15,000)^x c p = 15,000(0.96)^x d p = 15,000(1.04)^x

Explanation:

Step1: Recall exponential growth formula

The general formula for exponential growth is \( p = a(1 + r)^x \), where \( a \) is the initial amount, \( r \) is the growth rate (as a decimal), and \( x \) is the number of time periods.

Step2: Identify values from the problem

Here, the initial population \( a = 15,000 \) (in 2005, when \( x = 0 \)). The growth rate \( r = 4\% = 0.04 \). So \( 1 + r = 1 + 0.04 = 1.04 \).

Step3: Substitute into the formula

Substituting \( a = 15,000 \) and \( 1 + r = 1.04 \) into the exponential growth formula, we get \( p = 15,000(1.04)^x \).

Answer:

D. \( p = 15,000(1.04)^x \)