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 tow

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).

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Khang Minh 4 years 2021-09-01T01:51:26+00:00 1 Answers 7 views 0

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  1. giabao
    0
    2021-09-01T01:53:12+00:00
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    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

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