Question

Write an equation relating OO, the number of organisms in the lake (in millions), to time tt in years since 2010, given that every year the lake becomes more polluted, and 2% fewer organisms can live in it. In 2010, there were 1,200,000 organisms.

Answer 1

The equation that describes how the number of organisms in the lake decreases by 2% every year is OO = 1.2 * (0.98)^t, where OO is the number of organisms in millions, and t is the time in years since 2010.

Step-by-step explanation:

The equation relating OO, the number of organisms in the lake (in millions), to time t in years since 2010, when pollution reduces the number of organisms by 2% each year, and the initial population in 2010 was 1,200,000 (or 1.2 million), can be derived using an exponential decay model.

To model this situation, we start with the initial population, which we denote as OO0, being 1.2. The decay rate, which we will call r, is 2% or 0.02. The formula for exponential decay is OO = OO0 * (1 - r)^t. Therefore, we can write the equation for the population of organisms in the lake over time as OO = 1.2 * (0.98)^t.

This represents the exponential decay of the organism population over time due to increasing pollution levels in the lake.