Question

The population of an aquatic species in a certain body of water is approximated by the logistic\\ 22,500\\ function $G(t) = \frac{22,500}{1 + 10e^{-0.5t}}$, where $t$ is measured in years.\\ Calculate the growth rate after 5 years.\\ The growth rate in 5 years is $oxed{}$\\(Do not round until the final answer. Then round to the nearest whole number as needed.)

          The population of an aquatic species in a certain body of water is approximated by the logistic\\
22,500\\
function $G(t) = \frac{22,500}{1 + 10e^{-0.5t}}$, where $t$ is measured in years.\\
Calculate the growth rate after 5 years.\\
The growth rate in 5 years is $oxed{}$\\(Do not round until the final answer. Then round to the nearest whole number as needed.)
        
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The population of an aquatic species in a certain body of water is approximated by the logistic

22,500

function G(t) = (22,500)/(1 + 10e^-0.5t), where t is measured in years.

Calculate the growth rate after 5 years.

The growth rate in 5 years is oxed
(Do not round until the final answer. Then round to the nearest whole number as needed.)

Added by Jennifer M.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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The population of an aquatic species in a certain body of water is approximated by the logistic 22,500 functionG(t)= Ay 30,000 20,000 Calculate the growth rate after 5 years. G(I) 10.000 121620 The growth rate in 5years is[ Do not round until the final answer. Then round to the nearest whole number as needed
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Transcript

-
00:02 Water is approximated by the logistic function g of t.
00:05 We need to find the derivative of it, and then we can use the derivative function to find the growth rate in five years.
00:16 So we want to find ddt of 37 ,500 over 14e to the negative, i'm going to call it 16t over 25 plus 1, which would be equal to 37 ,000.
00:37 500 times d d t of 1 over 14 e to the negative 16 t over 25 plus 1 which would be negative 37 500 times d d t of 14 e to the negative 16 25 plus 1 over 14 e to the negative 16 25s t plus 1 over 14 e to the negative 16 25th t plus one squared, which would be negative 37 ,500 times 14 d, d .t of e to the negative 1625th t plus d, dt of 1 over 14e to the negative 1625th t, plus ddt of 1 over 14e to the negative 1625th t.
02:00 Plus 1 squared, which would be negative 37 ,500 times 14e to the negative 16t over 25 times ddt of negative 16t over 25 plus 0 over 14e to the negative 16 25 plus 0 over 14 e to the negative 16 25th t plus 1 squared.
02:37 And some simplifying now, that would be 52 ,000, or not 52 ,000, but 525 ,000 times negative 16, 25ths, times d, dt of t, times e to the negative 16, 25th's t...
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