Which of the following equations best represents the function for the situation "an initial population (P) of 1,400 people decreasing by 5% per year (x)"?
p=1,400-5x
p=1,400(0.05)^x
p=1,400(0.95)^x
p=1,400/5x
If 5% is gone, that leaves 95% of the previous population.
So, #3.
The correct equation that represents the situation is:
p = 1,400(0.95)^x
To explain how to arrive at this equation, let's break it down step by step:
1. We start with an initial population of 1,400 people, represented by 'P'.
2. The population is decreasing by 5% per year. To represent this decrease, we need to multiply the previous year's population by a factor of (1 - 0.05), which is equal to 0.95. So, the population at any given year 'x' will be 0.95 times the previous population.
3. Since the initial population is 1,400, we can write the equation as:
p = 1,400(0.95)^x
Here, 'p' represents the population at year 'x'.
Therefore, the correct equation is p = 1,400(0.95)^x. This equation describes a population that starts at 1,400 and decreases by 5% each year.