After years of maintaining a steady population of 32,000 , the population of a town begins to grow exponentially. After
1 year and an increase of per year, the population is 34,560 . Which equation can be used to predict, , the
number of people living in the town after years? (Round population values to the nearest whole number.)

Ask by Lynch Lowe. in the United States

Jan 24,2025

Question

After years of maintaining a steady population of 32,000 , the population of a town begins to grow exponentially. After
1 year and an increase of per year, the population is 34,560 . Which equation can be used to predict, , the
number of people living in the town after years? (Round population values to the nearest whole number.)

Ask by Lynch Lowe. in the United States

Jan 24,2025

UpStudy AI · Accepted Answer

The correct equation to model the population growth of the town is:

$$ y = 32,000 \times (1.08)^x $$

**Explanation:**

1. **Initial Population:** The town starts with a population of 32,000.
2. **Growth Rate:** The population grows exponentially at an annual rate of $$ 8\% $$, which is represented by the factor $$ 1.08 $$ (where $$ 1 $$ represents the original population and $$ 0.08 $$ represents the $$ 8\% $$ growth).
3. **Time Variable:** $$ x $$ represents the number of years after the population starts growing.
4. **Exponential Growth Formula:** The general form for exponential growth is:
   $$
   y = y_0 \times (1 + r)^x
   $$
   where:
   - $$ y $$ is the future population.
   - $$ y_0 $$ is the initial population (32,000 in this case).
   - $$ r $$ is the growth rate (0.08 for $$ 8\% $$).
   - $$ x $$ is the number of years.

Substituting the given values into the formula:
$$
y = 32,000 \times (1.08)^x
$$

This equation accurately models the population growth, ensuring that after each year, the population increases by $$ 8\% $$ of its current value.

**Answer:** 
$$ y = 32{,}000 \times (1.08)^x $$
The correct equation to predict the population after $$ x $$ years is: $$ y = 32,000 \times (1.08)^x $$

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