To model the declining llama population using an exponential equation, we can use the formula for exponential decay:

Question

\[
P(t) = P_0 \cdot (1 - r)^t
\]

where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population,
- \( r \) is the rate of decrease (as a decimal),
- \( t \) is the time in years.

Given:
- Initial population (\( P_0 \)) = 50,000 llamas
- Decrease rate (\( r \)) = 10% = 0.10
- Time (\( t \)) = 10 years

Now, we can plug these values into the formula:

\[
P(10) = 50000 \cdot (1 - 0.10)^{10}
\]

Calculating:

\[
P(10) = 50000 \cdot (0.90)^{10}
\]

Now, we calculate \( (0.90)^{10} \):

\[
(0.90)^{10} \approx 0.3487
\]

Thus,

\[
P(10) \approx 50000 \cdot 0.3487 \approx 17435
\]

Therefore, the population after 10 years would be approximately **17,435 llamas**.
make this like a 8th grader wrote it

Answer 1

To figure out how many llamas are left after a certain number of years when their population is slowly decreasing, we can use a formula called exponential decay. The formula looks like this:

\[ P(t) = P_0 \cdot (1 - r)^t \]

Here’s what the letters mean:

• \( P(t) \) is the llama population after time \( t \),
• \( P_0 \) is the starting number of llamas,
• \( r \) is how much the population decreases (as a decimal),
• \( t \) is the number of years.

Let’s say we start with 50,000 llamas. The population is going down by 10% each year, which we can write as 0.10 in decimal form. We want to find out how many llamas there are after 10 years.

So, we start by plugging our numbers into the formula:

\[ P(10) = 50000 \cdot (1 - 0.10)^{10} \]

This simplifies to:

\[ P(10) = 50000 \cdot (0.90)^{10} \]

Next, we need to calculate \( (0.90)^{10} \). When we do that, we find:

\[ (0.90)^{10} \approx 0.3487 \]

Now we can find out the new llama population:

\[ P(10) \approx 50000 \cdot 0.3487 \]

Calculating that gives us:

\[ P(10) \approx 17435 \]

So, after 10 years, there would be about 17,435 llamas left.