Final answer:
The equation for the world population after n years, given the growth rate of 1.167%, is P = 6.6 e^{0.01167n} . To estimate the world population in 2017, 10 years after 2007, the population is approximately 7.4 billion.
Step-by-step explanation:
The CIA estimates the world population is growing at a rate of 1.167% each year. The world population for 2007 was about 6.6 billion.
a. Write an equation for the world population after n years.
We will use the exponential growth formula P = P0ert, where P is the population after n years, P0 is the initial population (6.6 billion), r is the growth rate (1.167%, or 0.01167 when converted to a decimal), and t is the time in years. Our equation then becomes P = 6.6 e^{0.01167n}.
b. What will the estimated world population be in 2017?
To estimate the world population in 2017, we substitute n with 10 (since 2017 is 10 years after 2007) into our equation P = 6.6 e^{0.01167n}. Calculating this, we get an estimated world population of about 7.4 billion in 2017.