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.
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2 points
(1) 480, (2) 4000
(1) 45, (2) 4080
(1) 45, (2) 4000
(1) 480, (2) 4080

Answer 1

To determine the town's population in 1950 and the projected population in 2030 using the function \( f(n) = 480 + 45n \):

1. Population in 1950:

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

2. Projected Population in 2030:

   • The year 2030 is 80 years after 1950, so \( n = 80 \).
   • \( f(80) = 480 + 45 \cdot 80 = 480 + 3600 = 4080 \).
   • Therefore, the projected population in 2030 is 4080 people.

So, the correct answers are: (1) 480, (2) 4080.