Question

The number of mosquitoes at the beach has tripled every year since 1999. In 1999, there were 2,500 mosquitoes. Write a model for this situation. How many mosquitoes would you predict were at the beach in 2005?

a) Model: M=2500×3^(Y−1999)
b) Model: M=2500+3Y
c) Model: M=2500×Y
d) Model: M=2500×3^(2005−1999)

Answer 1

The correct model for the mosquito population growth is M=2500×3^(Y-1999), which is option a. Using this model, the predicted number of mosquitoes at the beach in 2005 would be 1,822,500.

Step-by-step explanation:

To model the growth of the mosquito population at the beach, which has tripled every year since 1999, we use exponential growth. The correct model for this situation would be M=2500×3^(Y−1999), where 'M' is the number of mosquitoes and 'Y' is the year. So, the model a is the correct one.

Using this model to predict the number of mosquitoes in 2005, we substitute Y with 2005:

M=2500×3(2005−1999)

M=2500×36

We calculate 36 which is 729, and then multiply by 2500 to get the prediction:

M = 2500 × 729 = 1,822,500

Therefore, the number of mosquitoes predicted for the year 2005 would be 1,822,500.