Question

In the year 2019, a scientist determined there were 3,000 of a certain type

of fish in a lake. The table shows the fish population in the lake increased
exponentially at a rate of 10% each year. Based on this information, which
equation can be used to predict the fish population 3 years after 2019?

Answer 1

To predict the fish population in 2022, an exponential growth formula P(t) = P0 * (1 + r)^t is used, where P0=3,000 fish, r=10%, and t=3 years. The estimated fish population in 2022 would be about 3,993 fish.

Step-by-step explanation:

To predict the fish population 3 years after 2019 and knowing that the fish population increased exponentially at a rate of 10% each year, we will use the exponential growth formula:

P(t) = P0 * (1 + r)^t

Where:

• P(t) is the future population after time t,
• P0 is the initial population,
• r is the growth rate (as a decimal), and
• t is the time in years since the start.

Given:

• P0 = 3,000 fish,
• r = 10% = 0.10, and
• t = 3 years (2022).

The equation to predict the fish population in 2022 is:

P(3) = 3,000 * (1 + 0.10)^3

Now we calculate:

• P(3) = 3,000 * (1.1)^3
• P(3) = 3,000 * 1.331
• P(3) = 3,993 fish (approximately)

Thus, the population of fish in the lake in 2022 would be approximately 3,993, assuming a consistent annual growth rate of 10%.