Question

In the year 2005, a total of 7.1 million passengers took a cruise vacation. The global cruise industry has been growing at 10% per year for the last decade. Assume that this growth rate continues. Write a formula for to approximate the number, N, of cruise passengers (in millions) t years after 2005.

Answer 1

To approximate the number of cruise passengers t years after 2005, with an initial amount of 7.1 million passengers and a 10% growth rate, the formula is N = 7.1(1.10)^t.

Step-by-step explanation:

The student has asked for a formula to approximate the number of cruise passengers in millions, N, t years after 2005. Given the initial amount of 7.1 million passengers and the annual growth rate of 10%

To calculate the number of passengers in any given year after 2005, we can use the formula for exponential growth:

N = P(1 + r)^t

Where:

• P is the initial amount (7.1 million)
• r is the growth rate (0.10 for 10%)
• t is the number of years since 2005

Thus, the formula simplifies to:

N = 7.1(1.10)^t

Using this formula, we can estimate the number of passengers for any year after 2005 by plugging in the number of years since 2005 as t.