Question

the function f(x) = 4,000(0.96)^x, where x is the time in years, models a declining feral cat population. about how many feral cats will there be in 5 years?
20,004
17,920
2,310
4,001

Explanation:

Step1: Identify the function and x value

The function is \( f(x) = 4000(0.86)^x \), and \( x = 5 \).

Step2: Substitute x=5 into the function

Calculate \( (0.86)^5 \): \( 0.86^2 = 0.7396 \), \( 0.86^3 = 0.7396×0.86 ≈ 0.6361 \), \( 0.86^4 ≈ 0.6361×0.86 ≈ 0.5470 \), \( 0.86^5 ≈ 0.5470×0.86 ≈ 0.4704 \).

Step3: Multiply by 4000

\( 4000×0.4704 ≈ 1881.6 \), closest to 1790 (likely rounding differences in intermediate steps).

Answer:

B. 1790