Question

fill in the blank 4 points a city has a population of 7000. its population is decreasing at a rate of 1.75%. this scenario can be represented by which of the following exponential functions? f(x) = 7000(1 - 0.0175) this equation simplifies to: f(x) = (type your answer...) (type your answer...)^x this scenario represents (choose your answer...)

Explanation:

Step1: Identify decay function form

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

Step2: Substitute given values

$P=7000$, $r=0.0175$, so $f(x)=7000(1-0.0175)^x$.

Step3: Simplify the base

Calculate $1-0.0175 = 0.9825$, so $f(x)=7000(0.9825)^x$.

Step4: Classify the scenario

This is exponential decay (population decrease over time).

Answer:

1. The correct exponential function: $\boldsymbol{f(x) = 7000(1-0.0175)^x}$
2. Simplified equation: $\boldsymbol{f(x) = 7000(0.9825)^x}$
3. Scenario classification: exponential decay