Question

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.

Answer 1

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

Answer 2

• r = 0.9433

Explanation:

Substitute the values into equation and solve for r:

• y = 5e^(rt)
• 7000000 = 5e^(2015 - 2000)r
• e^(15r) = 7000000/5
• e^(15r) = 1400000
• 15r = ln 1400000
• 15r = 14.15
• r = 14.15/15
• r = 0.9433