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 $f(x)=4423(0.9964)^x$.
the approximate population of the city in 2020 will be .
(round to the nearest whole number as needed.)

Explanation:

Step1: Calculate years after 1999

$x = 2020 - 1999 = 21$

Step2: Substitute x into decay function

$f(21) = 4423(0.9964)^{21}$

Step3: Compute the exponential term

$(0.9964)^{21} \approx e^{21 \times \ln(0.9964)} \approx e^{21 \times (-0.003606)} \approx e^{-0.0757} \approx 0.9267$

Step4: Calculate final population

$f(21) \approx 4423 \times 0.9267 \approx 4099$

Answer:

The exponential decay function is $f(x) = 4423(0.9964)^x$, and the approximate population in 2020 is 4099.