Problem

The population growth of an animal species is described by $F(t)=400 \log (2 t+3)$ where $t$ is measured in months. Find the population of this species in an area 6 months after the species is introduced. A. 240 B. 704 C. 74 D. 470

Solution

Step 1 :The population growth of an animal species is described by the equation \(F(t)=400 \log (2 t+3)\), where \(t\) is measured in months. We are asked to find the population of this species in an area 6 months after the species is introduced. This means we need to find the value of \(F(t)\) when \(t=6\). We can do this by substituting \(t=6\) into the equation.

Step 2 :Substitute \(t=6\) into the equation to get \(F(6)=400 \log (2 \times 6+3)\).

Step 3 :The result from the calculation is not matching with any of the options provided in the question. This could be due to the base of the logarithm used in the calculation. In the context of the question, it is not specified which base is used for the logarithm. If the base of the logarithm is 10, we need to adjust our calculation.

Step 4 :Adjust the calculation to use a logarithm base of 10 to get \(F(6)=400 \log_{10} (2 \times 6+3)\).

Step 5 :The population of the species 6 months after it is introduced is approximately 470. Therefore, the correct answer is \(\boxed{470}\).

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Source: https://solvelyapp.com/problems/20605/

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