Question

In the year 2003, a total of 7.2 million passengers took a cruise vacation. The global cruise industry has been growing at 9% per year for the last decade. Assume that this growth rate continues.(a) Write a formula for to approximate the number, N, of cruise passengers (in millions) t years after 2003.N= help (formulas)(b) How many cruise passengers (in millions) are predicted in the year 2011?N= help (numbers)(c) How many cruise passengers (in millions) were there in the year 2000?N= help (numbers)

Answer 1

The number of cruise passengers follows the exponential growth formula N = 7.2 * (1 + 0.09) ^ t. Using this, it's predicted that there were 13.547 million passengers in 2011 and 5.355 million passengers in 2000.

Step-by-step explanation:

The number of cruise vacation passengers growing at a 9% annual rate is a scenario of exponential growth. The general formula for exponential growth is N = P*(1 + r)^t, where N is the future value, P is the present value, r is the rate of growth, and t is time in years.

(a) To approximate the number of cruise passengers t years after 2003, replace P with 7.2 (the number of passengers in millions), r with 0.09 (9% growth rate), and t with the number of years since 2003. The formula then becomes N = 7.2 * (1 + 0.09) ^ t.

(b) In 2011, t equals 8 (2011 is 8 years after 2003). Replacing t with 8 in the formula, we get N= 7.2 * (1 + 0.09) ^ 8 = 13.547 million cruise passengers predicted in 2011.

(c) The year 2000 is 3 years before 2003. Exponential growth can be reversed to calculate previous years by using a negative t. So, for 2003, t is -3. When you put these values into our formula, it becomes N = 7.2 * (1 + 0.09) ^ -3 = 5.355 million cruise passengers in 2000.

Learn more about Exponential Growth