logarithms

Question

The population N(t) (in millions) of a country t years after 1980 may be approximated by the formula
N(t) = 211e^0.0109t.
When will the population be twice what it was in 1980? (Round your answer to one decimal place.)

Please help solve thanks!

Answer 1

N(t) = 211e^0.0109t

 

For 1980, t=0 and N(t) = 211.  This is the population in 1980.  We want to know when the population will be twice as big, so we want N(t) = 2*211.  Let's plug that into the population equation and solve for t:

 

2*211 = 211e^0.0109t

2 = e^0.0109t

ln(2) = 0.0109t

ln(2)/0.0109 = t

 

Use your calculator to compute the answer.