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 Reese Turnbull. 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 Reese Turnbull. in the United States

Jan 24,2025

UpStudy AI · Accepted Answer

To determine the correct equation that predicts the population $$ y $$ of the town after $$ x $$ years, we need to analyze the information given:

1. The initial population is $$ 32,000 $$.
2. The population increases by $$ 8\% $$ per year.
3. After 1 year, the population is $$ 34,560 $$.

### Step 1: Understanding Exponential Growth

The general formula for exponential growth is given by:

$$
y = P(1 + r)^x
$$

where:
- $$ P $$ is the initial population,
- $$ r $$ is the growth rate (as a decimal),
- $$ x $$ is the number of years,
- $$ y $$ is the population after $$ x $$ years.

### Step 2: Identify Parameters

From the problem:
- Initial population $$ P = 32,000 $$
- Growth rate $$ r = 0.08 $$ (which is $$ 8\% $$)

### Step 3: Formulate the Equation

Substituting the values into the exponential growth formula, we get:

$$
y = 32,000(1 + 0.08)^x
$$

This simplifies to:

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

### Step 4: Verify with Given Information

After 1 year ($$ x = 1 $$):

$$
y = 32,000(1.08)^1 = 32,000 \times 1.08 = 34,560
$$

This matches the population given after 1 year.

### Conclusion

The correct equation to predict the population $$ y $$ after $$ x $$ years is:

$$
\boxed{y = 32,000(1.08)^{x}}
$$

Thus, the answer is:

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

Solución de inteligencia artificial de Upstudy

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Solución

Step 1: Understanding Exponential Growth

Step 2: Identify Parameters

Step 3: Formulate the Equation

Step 4: Verify with Given Information

Conclusion

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