Question

The equation p = 5,000 * 2^t represents the population of an invasive fish species in a large lake, t years since 2005, when the fish population in the lake was first surveyed. What is the population when t is -2?

A) 2,500
B) 1,250
C) 625
D) 312.5

Answer 1

To find the population at t = -2, you substitute -2 for t in the equation, calculate 2^(-2), and then multiply by 5,000. The result is a population of 1,250, which corresponds to option B.

Step-by-step explanation:

The equation p = 5,000 \* 2^t represents the population of an invasive fish species in a large lake, t years since 2005, when the fish population in the lake was first surveyed. To find the population when t is -2, we need to substitute -2 into the equation for t.

Step 1: Substitute t = -2 into the equation: p = 5,000 \* 2^(-2)

Step 2: Calculate the value of 2^(-2): 2^(-2) = 1 / (2^2) = 1 / 4 = 0.25

Step 3: Multiply 5,000 by 0.25: p = 5,000 \* 0.25 = 1,250

Therefore, when t is -2, the population of the invasive fish is 1,250, which is option B).