The population N(t) (in millions) of the United States t years after 1980 may be approximated by the formula N(t)=762e^0.022t. WHen will the population reach 1.5 billion?

Answer 1

By substituting 1.5 billion in for N(t) and taking the natural log (ln) of both sides, you'll find your answer.

N(t) = 762e^0.022t

1,500,000,000 = 762e^0.022t (Substitute)

(1,500,000,000 = 762e^0.022t)/(762) Divide both sides by 762

1,968503.937 = e^0.022t (Apply the natural log of both sides of the equation)

ln(1,968503.937) = ln(e^0.022t)

14.943 = 0.022t (Solve for t by dividing both sides by 0.022)

t = 658.763 years

1980 + 658.763 = 2638.763 So approximately October of 2638.

Hope this helps. Good luck!