Use the logistic growth model $f(x)=\frac{130}{1+5 e^{-2 x}}$. Find the carrying capacity.
Final Answer: The carrying capacity of the logistic growth model \(f(x)=\frac{130}{1+5 e^{-2 x}}\) is \(\boxed{130}\).
Step 1 :Use the logistic growth model \(f(x)=\frac{130}{1+5 e^{-2 x}}\). Find the carrying capacity.
Step 2 :The carrying capacity in a logistic growth model is the maximum value that the function can reach.
Step 3 :In the given logistic growth model \(f(x)=\frac{130}{1+5 e^{-2 x}}\), the carrying capacity is the value of the function as \(x\) approaches infinity.
Step 4 :This is because as \(x\) gets larger and larger, the exponential term \(e^{-2x}\) gets closer and closer to zero, and the function approaches its maximum value.
Step 5 :Therefore, the carrying capacity is the coefficient of the numerator, which is 130 in this case.
Step 6 :Final Answer: The carrying capacity of the logistic growth model \(f(x)=\frac{130}{1+5 e^{-2 x}}\) is \(\boxed{130}\).