A small town started to track its population in the year 1950. Each year that passed, the town's population increased by 45. The function ƒ(n) = 480 + 45n represents the town population n years after 1950. What was the town's population in 1950? What is the projected population in 2030?

Question

The town's population in 1950 was (1)___________ people. The projected population in 2030 is (2)____________ people.
*
2 points
(1) 480, (2) 4000
(1) 45, (2) 4080
(1) 45, (2) 4000
(1) 480, (2) 4080

Answer 1

To find the town's population in 1950 and the projected population in 2030, we can analyze the function given: \( f(n) = 480 + 45n \).

1. Population in 1950 (n = 0):

   • In 1950, \( n = 0 \).
   • So, \( f(0) = 480 + 45(0) = 480 \).
   • Therefore, the town's population in 1950 was 480 people.

2. Projected population in 2030:

   • To find \( n \) for 2030, we calculate the number of years since 1950.
   • 2030 - 1950 = 80 years, so \( n = 80 \).
   • Now, we calculate the population: \[ f(80) = 480 + 45(80) = 480 + 3600 = 4080. \]
   • Thus, the projected population in 2030 is 4080 people.

Putting it all together, we have:

The town's population in 1950 was (1) 480, and the projected population in 2030 is (2) 4080.

So the answer is: (1) 480, (2) 4080.