Question

Pedro is hosting a pizza party for his basketball team. The more team members who attend the party, the more pizzas he will need to order.

t= the number of team members who attend the pizza party
p= the number of pizzas Pedro will need to order

Which of the variables is independent and which is dependent?
A. t is the independent variable and p is the dependent variable
B. p is the independent variable and t is the dependent variable

Answer 1

To predict the population of Cary in 2008 using the uninhibited growth model, first calculate the growth rate based on 1980 and 1987 data, and then apply the rate to predict the 2008 population. The predicted population is approximately 119,700.

Step-by-step explanation:

The student asks for a prediction of the population of Cary for the year 2008 using the uninhibited growth model. Here, we'll use an exponential growth model since the assumption is that the population grows without bounds. The general formula for exponential growth is P(t) = P0ert, where P(t) is the population at time t, P0 is the initial population, r is the growth rate, and t is the time in years since the initial population was measured.

To predict the population for Cary in the year 2008, we'll first need to find the growth rate (r). We do this by using the provided population data for Cary from 1980 and 1987. We will then apply the growth rate to predict the population for 2008.

First, we determine 'r' using the formula:

39387 = 21763er(7), where 7 is the number of years between 1980 and 1987.

Next, we solve for r:

r = ln(39387/21763)/7 ≈ 0.0609

Lastly, we use the growth rate to predict the population for 2008:

P(2008) = 21763e0.0609(28) (since 2008 is 28 years from 1980).

This results in:

P(2008) = 21763e1.7052 ≈ 21763 * 5.503 ≈ 119,700 (rounded to the nearest whole number).

Therefore, the predicted population of Cary in 2008 using the uninhibited growth model is approximately 119,700.