Question

Please answer this quickly!

Ajay is researching how the population of his hometown has changed over time. Specifically, he learns his hometown had a population of 20{,}00020,000 in 1990, and that the population has since increased by about 8% every 3 years.

Ajay predicts that his town can only support a population of 50,000. Ajay is relieved to see that population has not exceeded
50,000 t years after 1990.
Write an inequality in terms of ttt that models the situation.

Answer 1

Answer:20,000⋅(1.08)^t/3≤50,000

Answer 2

Inequalities help us to compare two unequal expressions. The inequality in terms of t years is written as 20,000[(1.08)^(t/3)]≤50,000.

What are inequalities?

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

Given that Ajay's hometown population in the year 1990 is 20,000, which increases by 8% every 3 years, therefore, we can write the expression for the population after t years as,

Population after t years

$= 20,000(1+8\%)^{\dfrac t3}\\\\= 20,000(1.08)^{\dfrac t3}$

Also, it is given that Ajay's hometown does not support a population of more than 50,000. Now, after t years the population of the town has not exceeded 50,000. Therefore, we can write about inequality as,

Population after t years ≤ 50,000

$20,000(1.08)^{\dfrac t3} \leq 50,000$

Hence, the inequality in terms of t years is written as $20,000(1.08)^{\dfrac t3} \leq 50,000$.

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