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the logistic growth model...represents the number of families that own a home in a certain small (but growing) ciry t years after 1980. in what year did 2,335 families own a home?

the logistic growth modelrepresents the number of families that own a home in a certain small but growing ciry t years after 1980 in what year did 2335 families class=

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tramserran

Answer: 1982

Explanation:

H(t) = [tex]\frac{7000}{1 + 6e^{-0.55t}}[/tex]

2335 = [tex]\frac{7000}{1 + 6e^{-0.55t}}[/tex]

2335[tex](1 + 6e^{-0.55t})[/tex] = 7000

[tex]1 + 6e^{-0.55t}[/tex] = [tex]\frac{7000}{2335}[/tex]

[tex]6e^{-0.55t}[/tex] = [tex]\frac{7000}{2335}-1[/tex]

[tex]6e^{-0.55t}[/tex] = [tex]\frac{7000}{2335}-\frac{2335}{2335}[/tex]

[tex]6e^{-0.55t}[/tex] = [tex]\frac{4665}{2335}[/tex]

[tex]e^{-0.55t}[/tex] = [tex]\frac{4665}{2335(6)}[/tex]

[tex]e^{-0.55t}[/tex] = [tex]\frac{1}{2}[/tex]

[tex]lne^{-0.55t}[/tex] = [tex]ln\frac{1}{2}[/tex]

-0.55t = ln[tex]\frac{1}{2}[/tex]

t = [tex]\frac{ln\frac{1}{2}}{-0.55}[/tex]

t = 2

Year: 1980 + t   = 1980 + 2   = 1982

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