Question

In 2014, a town's population was 795 people. By 2020, the population had grown to 1262 people. a. Create an exponential equation for the town's population "n" years from 2014. Round your multiplier to the nearest hundredth (2 decimal places).

Answer 1

Answer: $P=795(1.84)^n$

Step-by-step explanation:

Given

Initial population was $795$ people

By 2020, it becomes $1262$ people

Suppose the population follows the trend $P=P_oa^{n}$

where, $n$ is the number of years after 2014

For year 2020 it is 6. Insert the values

$\Rightarrow 1262=795a^{6}\\\\\Rightarrow 1.587=a^{6}\\\\\text{Taking log both sides}\\\\\Rightarrow \log (1.587)=6\log (a)\\\Rightarrow \log (a)=0.2645\\\\\Rightarrow a=10^{0.2645}\\\Rightarrow a=1.84$

Thus, the exponential population trend is $P=795(1.84)^n$