Question

In 1960, the population of a town was 14 thousand people. Over the course of the next 50 years, the town grew at a rate of 30 people per year. Hint: let t=0 be 1960, and t-1 be 1961, etc. A) Assuming this continues, what is the population predicted to be in 2030? B) Set up and solve the equation to find in which year the population will reach 15 thousand. Give your answer in a form like 1980 or 1994. A) B Question Help: D Post to forum Submit Question people

Answer 1

SOLUTIONS

Given: Assume y is the population

$\begin{gathered} t=0=1960,y=14030 \\ t=1=1961,y=14060 \\ so\text{ b = 14000} \\ so\text{ k = 30} \end{gathered}$

The town grow at the rate of 30 people per year.

$y=kt+14000$$y=30t+14000$

(A) The population predicted to be in 2030 will be

$\begin{gathered} 2030-1960=70 \\ y=30k+14000 \\ y=30(70)+14000 \\ y=2100+14000 \\ y=16100people \end{gathered}$

(B) so when y = 15000, find t

$\begin{gathered} y=15000 \\ y=30t+14000 \\ 15000=30t+14000 \\ 15000-14000=30t \\ 1000=30t \\ t=\frac{1000}{30} \\ t\approx33 \\ t=1960+33 \\ t=1993 \end{gathered}$