Question

a city has a population of 7000. its population is decreasing at a rate of 1.25%. this scenario can be represented by which of the following exponential functions? f(x) = choose your answer... ^x choose your answer... 7000(1 - 0.0175) 7000(1.014) 7000(1.012) 7000(0.9875) 1.75(1 + 0.028) 7000(0.969) use the table to the correct exponential function.

Explanation:

Step1: Recall decay function form

The general exponential decay function is $f(x) = P(1-r)^x$, where $P$ is initial population, $r$ is decay rate.

Step2: Identify given values

$P=7000$, $r=1.25\%=0.0125$

Step3: Calculate decay factor

$1-r = 1-0.0125 = 0.9875$

Step4: Form the function

Substitute values into the decay formula: $f(x)=7000(0.9875)^x$

Answer:

$7000(0.9875)$ (with the implicit exponent $x$ for time periods)