Question

the population of a certain city was 4,423 in 1999. it is expected to decrease by about 0.36% per year. write an exponential decay function, and use it to approximate the population in 2020.
the exponential decay function where f(x) is the population of the city x years after 1999 is f(x) = □.

Explanation:

Step1: Define decay function form

The general exponential decay function is $f(x) = P_0(1-r)^x$, where $P_0$ is the initial population, $r$ is the decay rate, and $x$ is time in years.

Step2: Identify given values

$P_0 = 4423$, $r = 0.0036$ (converted from 0.36%)

Step3: Substitute into function

$f(x) = 4423(1-0.0036)^x = 4423(0.9964)^x$

Step4: Calculate x for 2020

$x = 2020 - 1999 = 21$

Step5: Compute 2020 population

$f(21) = 4423(0.9964)^{21}$
First calculate $0.9964^{21} \approx 0.9297$, then $4423 \times 0.9297 \approx 4112$

Answer:

The exponential decay function is $f(x) = 4423(0.9964)^x$.
The approximate population in 2020 is 4112.