There is a protected species of bird living in the desert. There are only 1,234 birds left, and they are decreasing at a rate of 20 percent each year. Which of the following equations would you use to model this situation?(1 point)

Question

Responses

f(x)=(1,2340×0.2)x
f of x is equal to open paren 1 comma 2340 times 0 point 2 close paren to the x th power

f(x)=1,234(0.8)x
f of x is equal to 1 comma 234 0 point 8 x

f(x)=1,234(0.2)x
f of x is equal to 1 comma 234 times 0 point 2 to the x th power

f(x)=1,234(0.8)x

Answer 1

To model the situation where there are 1,234 birds left and they are decreasing at a rate of 20 percent each year, we need to find an exponential decay model.

Since the population decreases by 20 percent each year, it retains 80 percent of its population. Therefore, we can represent the remaining population as 80 percent of the original population, which can be expressed as \(0.8\) times the current number of birds.

The correct model for the remaining population after \(x\) years would then be:

\[ f(x) = 1,234 \times (0.8)^x \]

Thus, the correct response is:

f(x) = 1,234(0.8)^x