Question 1204452
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Suppose that the number of bacteria in a certain population increases according 
to a continuous exponential growth model. A sample of 2600 bacteria selected 
from this population reached the size of 2685 bacteria in one and a half hours. 
Find the hourly growth rate paramete
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<pre>
The exponential growth model is

    N = {{{N[0]*b^t}}},


{{{N[0]}}} is the initial population size, t is the time, "b" is the base of the exponential function.


For your problem, {{{N[0]}}} = 2600, t= 1.5 hours, N= 2685, so the equation takes the form

    2685 = {{{2600*b^1.5}}}.


Only base "b" is an unknown.  To find b, make these standard manipulations, step by step

    {{{2685/2600}}} = {{{b^1.5}}}

    1.032692308 = {{{b^1.5}}}

    log(1.032692308) = 1.5*log(b)

    log(b) = {{{log((1.032692308))/1.5}}} = 0.009313961

    b = {{{10^0.009313961}}} = 1.021677811


<U>ANSWER</U>.  The base, or the exponential hourly rate of growth in this problem is 1.021677811.

         You may round it to 1.00931, for example.
</pre>

Solved.