Question

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?

Answer 1

Answer: 1982

Step-by-step explanation:

H(t) =
`(7000)/(1 + 6e^(-0.55t))`

2335 =
`(7000)/(1 + 6e^(-0.55t))`

2335
`(1 + 6e^(-0.55t))` = 7000

`1 + 6e^(-0.55t)` =
`(7000)/(2335)`

`6e^(-0.55t)` =
`(7000)/(2335)-1`

`6e^(-0.55t)` =
`(7000)/(2335)-(2335)/(2335)`

`6e^(-0.55t)` =
`(4665)/(2335)`

`e^(-0.55t)` =
`(4665)/(2335(6))`

`e^(-0.55t)` =
`(1)/(2)`

`lne^(-0.55t)` =
`ln(1)/(2)`

-0.55t = ln
`(1)/(2)`

t =
`(ln(1)/(2))/(-0.55)`

t = 2

Year: 1980 + t = 1980 + 2 = 1982