use a graphing calculator and the following scenario. the population p of a fish farm in t years is modeled…

use a graphing calculator and the following scenario. the population p of a fish farm in t years is modeled by the equation ( p(t)=\frac{1900}{1 + 9e^{-0.6t}} ). to the nearest whole number, what will the fish population be after 2 years? fish

use a graphing calculator and the following scenario. the population p of a fish farm in t years is modeled by the equation ( p(t)=\frac{1900}{1 + 9e^{-0.6t}} ). to the nearest whole number, what will the fish population be after 2 years? fish

Answer

Explanation:

Step1: Substitute (t = 2) into the formula

Substitute (t = 2) into (P(t)=\frac{1900}{1 + 9e^{-0.6t}}), we get (P(2)=\frac{1900}{1+9e^{-0.6\times2}}). First, calculate the exponent: (-0.6\times2=-1.2). Then, calculate (e^{-1.2}). Using the property (a^{-b}=\frac{1}{a^{b}}), (e^{-1.2}=\frac{1}{e^{1.2}}\approx\frac{1}{3.320117}\approx0.3012).

Step2: Calculate the denominator

Calculate (1 + 9e^{-1.2}). Substitute (e^{-1.2}\approx0.3012) into it: (1+9\times0.3012=1 + 2.7108=3.7108).

Step3: Calculate (P(2))

Now, calculate (P(2)=\frac{1900}{3.7108}\approx512).

Answer:

(512)