Point slope Form - Town Population

Question

A town's population increases at a constant rate. In 2002 the population was 67,632. By 2019 the population had increased to 214,682. Assume this trend continues.

Predict the population in 2025.

Identify the year in which the population will reach 298,000.

Answer 1

2002 67,632 population

2019 214,682 population

what is pop in 2025??

what year 292,000??

rate of change per year = y's/x's = (292K-67.632K)/(19-12) = 124.368K/7

= about 17.767K = 17,767 per year pop increase

in 2025 that's 6 more years since 2019. 6x17,767 then add to 214, 682

= 321,284

when 292,000? less than 2025, more than 2019

292,000 - 214,682 = 78,318

divide by 17,767 = about 4.4 years

2019 + 4.4 = 2023.4 is when pop reaches 292,000

round to nearest integer = 2023

but it really reaches 292,000 about 4 months into 2024

Answer 2

Hi Joshua,

If you set the year 2000 to zero, then your data can be organized into these ordered pairs:

(2, 67632)

(19, 214682)

(21, _______?).

The question suggests that the population is changing by the same amount each year, and there will be two more years of growth at that pace after 2019.

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