Question

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Using a Model from a Sequence Practice
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Question
A small town started to track its population in the year 1950. Each year that passed, the town’s population increased by 44. The function f(n)=495+44n
represents the town population n years after 1950. What was the town’s population in 1950? What is the projected population in 2030?(1 point)
The town’s population in 1950 was
people. The projected population in 2030 is
people.

Answer 1

To find the town's population in 1950 and project the population in 2030 using the function \( f(n) = 495 + 44n \):

1. **Population in 1950**: When \( n = 0 \) (which represents the year 1950),
\[
f(0) = 495 + 44(0) = 495
\]
So, the town’s population in 1950 was **495** people.

2. **Projected population in 2030**: In 2030, \( n \) will be 80, since 2030 - 1950 = 80.
\[
f(80) = 495 + 44(80) = 495 + 3520 = 4015
\]
Therefore, the projected population in 2030 is **4015** people.

Putting it all together:
- The town’s population in 1950 was **495** people.
- The projected population in 2030 is **4015** people.