To predict the population of the endangered flowering plant species after 10 years using the given equation \( y = 49.550(0.766)^x \), we can substitute \( x = 10 \) into the equation:
\[ y = 49.550(0.766)^{10} \]
Now let's calculate \( (0.766)^{10} \):
\[ (0.766)^{10} \approx 0.1044 \]
Now, let's multiply this value by 49.550:
\[ y \approx 49.550 \times 0.1044 \approx 5.179 \]
Since the values are in thousands, we convert this result back to the actual number of plants:
\[ y \approx 5.179 \times 1000 \approx 5179 \]
Thus, the predicted population is approximately 5179 plants, or about 5000 plants when rounded.
Looking at the provided options:
a. the model predicts that the plant population will be about 2000 plants after 10 years have passed
b. the model predicts that the plant population will be about 6000 plants after 10 years have passed
c. the model predicts that the plant population will be about 3000 plants after 10 years have passed
d. the model predicts that the plant population will be about 4000 plants after 10 years have passed
The closest option to approximately 5179 plants is b. the model predicts that the plant population will be about 6000 plants after 10 years have passed.