Question

Rosario is an ecologist who studies the change in the penguin population of Antarctica over time.

The relationship between the elapsed time t, in years, since Rosario started studying the population, and
the number of penguins, P(t), is modeled by the following function:

P(t) = 21,000 • (4/7)^t/3
Complete the following sentence about the rate of change in the penguin population.

The population of penguins loses 3/7 of its size every ____ years.

Answer 1

Answer: every 3 years

Explanation:

Answer 2

The penguin population loses 3/7 of its size every 3 years according to the function P(t) = 21,000 • (4/7)ᵗ/³.

The given function describing the penguin population is P(t)=21,000.(4/7)ᵗ/³ . To determine the rate of change in the penguin population, observe the exponent (t/3) in the function. This exponent governs how the population changes over time. The base 4/7 in the function represents the ratio of the population decreasing each time interval.Specifically, the population decreases by 3/7 of its size after every t/3,where the time interval is 3 years. Therefore, every 3 years 3/7 of the penguin population is lost, which indicates that the population of penguins loses 3/7 of its size every 3 years.