Question

The fish population in a local lake is 10,000. The population increases by half every year. Which function represents the fish population after X years?

A) None of these
B) f(x)=1.5(10,000)ˣ
C) 10,000(-1.5)ˣ
D) f(x)=10,000(1.5)ˣ
E) f(x)=10,000(0.5)ˣ

Answer 1

The function that represents the fish population after X years in this case is f(x) = 10,000(1.5)^x.

Step-by-step explanation:

The question asks to determine the function that represents the fish population in a lake after X years, given that the population starts at 10,000 and increases by half every year. To find this function, we need to express the population growth as a mathematical formula where the base population is multiplied by the growth rate raised to the power of the number of years that have passed (X).

In this scenario, the growth rate is 1.5 (or 150%) because the population increases by half (50%) each year. Thus, the initial population must be multiplied by 1.5 each year. The correct function therefore takes the initial population and multiplies it by 1.5 to the power of X, which gives us the formula f(x) = 10,000(1.5)x.