Question 1197950
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A population of bacteria is growing according to the equation
P(t)=1950e^0.07t. Estimate when the population will exceed 3010.
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<pre>
Write inequality

    3010 < {{{1950*e^(0.07*t)}}}.


Divide both sides by 1950

    {{{3010/1950}}} < {{{e^(0.07*t)}}},


which is the same as

    {{{1.543589744}}} < {{{e^(0.07*t)}}}.


Take logarithm base 10 of both sides

    log(1.543589744) < 0.07*t.


Express t and calculate

    t > {{{log((1.543589744))/0.07}}} = 2.693312634.


Round with 4 decimals  t = 2.6933.    <U>ANSWER</U>


The problem does not provide the name of the time units,
so I can not name the unit of the time in my answer.
</pre>

Solved.


What you see in my post, is a standard procedure for solving such problems.


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To see many other similar and different solved problems on bacteria growth, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/logarithm/Bacteria-growth-problems.lesson>Bacteria growth problems</A> 

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic "<U>Logarithms</U>".



Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.