Question

19) In the formula N = lekt, N is the number of items in terms of an initial population I at a given time t

and k is a growth constant equal to the percent of growth per unit time. How long will it take for
the population of a certain country to double if its annual growth rate is 3.4% ? Round to the nearest
year.
I

Answer 1

To calculate the time for a population to double with a 3.4% annual growth rate, use the rule of 70 where you divide 70 by the growth rate. In this case, it will take approximately 21 years for the population to double, after rounding to the nearest year.

Step-by-step explanation:

The student has asked how long it will take for the population of a certain country to double if its annual growth rate is 3.4%. To find the doubling time, we can use the rule of 70, which states that the doubling time (t) in years can be approximated by dividing 70 by the annual percentage growth rate.

In this case, the formula is:

t = 70 / k

Where k is expressed as a whole number, not a decimal. So the growth rate of 3.4% should be used as 3.4, not 0.034.

Substituting into the formula:

t = 70 / 3.4

t ≈ 20.59 years

Therefore, it will take approximately 21 years for the population to double, rounding to the nearest year as per the question request.