Question

The population

N(t) (in millions)
of a country t years after 1980 may be approximated by the formula
N(t) = 216e0.0109t.
When will the population be twice what it was in 1980? (Round your answer to one decimal place.)
t =

Answer 1

The population will double around the year 2048

Explanation:

Answer 2

So, the population will be twice what it was in 1980 approximately 63.6 years after 1980. Rounded to one decimal place, t is approximately 63.6 years.

Certainly! To find when the population will be twice what it was in 1980, we can set up the equation:

N(t)=2×N(0)

Given that N(t)=216e0.0109t and N(0) is the population in 1980, we substitute these values and solve for

216e 0.0109t=2×N(0)

Now, divide both sides by 216:

Take the natural logarithm (ln) of both sides to solve for t:

0.0109t=ln( 2162/×N(0)

Now, solve for t:

So, the population will be twice what it was in 1980 approximately 63.6 years after 1980. Rounded to one decimal place, t is approximately 63.6 years.