A small town started to track his population in the year 1950 each year the past the town's population increased by 44 the function f of n = 495 + 44 and represents a town population in years after 1950 what was the town's population in 1950 what is the projected population in 2030

Answer 1

To understand the problem, let's break it down step-by-step.

1. Population function interpretation: The function \( f(n) = 495 + 44n \) represents the population of the town \( n \) years after 1950.

2. Finding the population in 1950: In 1950, \( n = 0 \). \[ f(0) = 495 + 44 \cdot 0 = 495 \] Thus, the population of the town in 1950 was 495.

3. Finding the projected population in 2030: To find the population in 2030, we first need to determine how many years after 1950 that is. \[ 2030 - 1950 = 80 \] This means \( n = 80 \) for the year 2030.

   Now, substitute \( n = 80 \) into the population function: \[ f(80) = 495 + 44 \cdot 80 \] Calculate \( 44 \cdot 80 \): \[ 44 \cdot 80 = 3520 \] Now add this to 495: \[ f(80) = 495 + 3520 = 4015 \]

So, the projected population of the town in 2030 is 4015.