Question

what is a doubling time? suppose a population has a doubling time of 30 years. by what factor will it grow in 120 years?

choose the correct definition of a doubling time below.

a. the time required for each doubling in exponential growth.
b. the time required for each halving in exponential growth.
c. the time required for each doubling in linear growth.
d. the time required for each halving in linear growth.

Explanation:

Define doubling time

Doubling Time is the time required for a quantity to double in size. This concept applies specifically to Exponential Growth, where the quantity increases at a rate proportional to its current value, rather than linear growth. Therefore, the correct definition is the time required for each doubling in exponential growth.

Calculate the growth factor

Using the Doubling Time formula, the growth factor after a given time \(t\) is calculated as:

$$ \text{Growth Factor} = 2^{\frac{t}{T_d}} $$

where \(t = 120\) years is the total time and \(T_d = 30\) years is the doubling time.

Compute the final value

Substituting the given values into the growth factor formula:

$$ \text{Growth Factor} = 2^{\frac{120}{30}} = 2^4 = 16 $$

This means the population will grow by a factor of 16 in 120 years.

Answer:

Question 1

• (A) The time required for each doubling in exponential growth. (Correct answer)
• (B) The time required for each halving in exponential growth.
• (C) The time required for each doubling in linear growth.
• (D) The time required for each halving in linear growth.

Question 2

The population will grow by a factor of 16 in 120 years.