The Verhulst model for population growth specifies the reproductive rate of an organism as a function of the total population according to the following formula: where p is the total population in thousands of organisms, and are constants that depend on the particular circumstances and organism being studied, and is the reproduction rate in thousands of organisms per hour. If and , find .

Question

The Verhulst model for population growth specifies the reproductive rate of an organism as a function of the total population according to the following formula:  where p is the total population in thousands of organisms,  and  are constants that depend on the particular circumstances and organism being studied, and  is the reproduction rate in thousands of organisms per hour. If  and  , find  .

Quizplus · Accepted Answer

Using the formula given, we can rearrange to solve for the reproductive rate: 
11ebfe6a_2ccc_7f4c_96cc_0f70eaf0524b_TBX8650_11 = 11ebfe6a_2ccc_7f4e_96cc_7b18b77b5d05_TBX8650_11 * (1 - p/11ebfe6a_2ccc_7f4d_96cc_09a26bdc0b19_TBX8650_11)
Substituting in the given values, we get:
11ebfe6a_2ccc_7f4c_96cc_0f70eaf0524b_TBX8650_11 = 11ebfe6a_2ccc_7f4e_96cc_7b18b77b5d05_TBX8650_11 * (1 - p/500)
8.5 = 5 * (1 - p/500)
p/500 = 3.5/5
p = 700/5 = 140
Therefore, the answer is 11ebfe6a_2ccc_7f52_96cc_bf80b3f7bb27_TBX8650_11, which corresponds to 140.

The Verhulst Model for Population Growth Specifies the Reproductive Rate