Question

The population of goldfish in a marine farm is decreasing at the rate of 20 percent per year. The farm started with a goldfish population of 1,000.

Part A: Create an equation that gives the number of goldfish in the nth year.

a. N(n)=1000×(0.8)ⁿ

b. N(n)=1000×(1−0.2)ⁿ

c. N(n)=1000×(1+0.2)ⁿ

d. Not Mentioned

Answer 1

The correct equation for the population of goldfish in the nth year as it decreases by 20% per year is N(n) = 1000 × (0.8)^n; this is represented by option a, and option b is mathematically the same but less simplified.

Step-by-step explanation:

The equation to represent the number of goldfish in the nth year as the population decreases by 20 percent per year is given by an exponential decay function. The initial population is 1,000 goldfish, and each year we multiply this population by 80% (which is 100% - 20% decrease), to find the number of goldfish remaining. Therefore, the correct mathematical expression for the number of goldfish in the nth year is N(n) = 1000 × (0.8)^n, which corresponds to option a. Option a and b are mathematically equivalent as (1 - 0.2) equals 0.8; however, option a is the more simplified form of the equation.