Question

The population of a city is modeled by the function $y = 35000(0.94) {}^{t}$where y is the population of the city after t years starting in the year 2000. is the city's population increasing or decreasing

Answer 1

The city's population is decreasing

1) We need to pay attention to the factor in this exponential model.

$y=35000\left(0.94\right)^t$

2) Note that the factor that multiplies 35000 (the initial population) is lesser than 1. This indicates that this exponential model points out a population decay.

3) So, we can tell that

$\begin{gathered} y=35000(0.94)^1\Rightarrow y=32900 \\ y=35000\left(0.94\right)^2\Rightarrow y=30926 \\ (...) \end{gathered}$

Therefore, The city's population is decreasing