Question

The function p models the population, in thousands, of a certain city t years after 2005. according to the model, the population is predicted to increase by n % every 18 months. what is the value of n ?

Answer 1

The value of n can be determined using the exponential growth formula P = Po * e^(n*t), where P represents the predicted population, Po represents the initial population, t represents the number of years, and n represents the growth rate.

Step-by-step explanation:

The value of n can be determined by using the exponential growth formula:

P = Po * e^(n*t)

In this case, Po represents the initial population, t represents the number of years since 2005, and P represents the predicted population after t years. The question states that the population increases by n% every 18 months, which is equivalent to a growth factor of (1 + n/100) every 18 months.

By substituting the given information into the formula and solving for n, we can determine the value of n.

Answer 2

The value of n is 150.

Step-by-step explanation:

The given function models the population of a certain city after a given number of years. The population is predicted to increase by n% every 18 months. We need to find the value of n.

The formula for population growth is given by:

P = Po * e^(n*t)

where:

• P is the final population
• Po is the initial population
• n is the growth rate in decimal form
• t is the time in years

In this case, the population is predicted to increase by n% every 18 months. So, the growth rate, n, is actually given as a percentage.

Therefore, we need to convert n to decimal form by dividing it by 100:

n/100 = 18/12

Simplifying this equation, we have:

n/100 = 3/2

Now, cross multiply and solve for n:

n * 2 = 3 * 100

n = 300/2

n = 150

So, the value of n is 150.