The projected world population (in billions of people) t years after 2000 is modeled by the function y = 5e^rt. Determine the value of r if the
population in 2015 is 7 billion.

y = 5 e^r * t

Let y be the population in billions and t the value of elapsed years

7 =   5 e^r * t  is the equation being used where  t = 15

7/5 = e^r * t

ln 7/5 = r * t     taking ln of both sides

r = .336 / 15 = .0224

y = 5 e^(.0224 t)    is then our equation

Check  - suppose you want y at 2020

y = 5 e^(.0224 * 20)    would be the equation

y = 5 e^.449 = 7.83  billion - seems to be a reasonable answer

Step-by-step explanation:

Substitute the values into equation and solve for r: