Question 1178994
.
A city population of 170,000 grows continuously according to the model P = 170000e0.0285t
where P is the population t years after the year 2000. In what year does the population reach 250000?
~~~~~~~~~~~~~



<pre>
Your exponential formula for the population growth is


    P(t) = {{{170000*e^(0.0285*t)}}}.


Based on the condition, you write the equation for t as you read your text


    250000 = {{{17000*e^(0.0285*t)}}}.


Next, you divide both sides by 170000


    {{{250000/170000}}} = {{{e^(0.0285*t)}}},    or


    1.470 = {{{e^(0.0285*t)}}}.


Now, you take natural logarithm of both sides


    ln(1.470) = 0.0285*t


which gives you an expression for time "t"


    t = {{{ln(1.470)/0.0285}}}


Next you use your calculator and get


    t = 13.518  years   (rouned)      <U>ANSWER</U>


<U>ANSWER</U>.  13 years and  189 days.
</pre>

Solved, answered, explained and completed.


----------------


To see many other solved problems on exponential growth/decay, &nbsp;look into the lessons

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

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

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

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

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/logarithm/A-medication-decay-in-a-human%27s-body.lesson>A medication decay in a human's body</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/logarithm/Problems-on-appreciated-depreciated-values.lesson>Problems on appreciated/depreciated values</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/logarithm/Inflation-and-Salary-problems.lesson>Inflation and Salary 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 lessons are 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.



/////////////



Do not forget to post your &nbsp;"THANKS" &nbsp;to me for my teaching.