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

Explanation:

H(t) = $\frac{7000}{1 + 6e^{-0.55t}}$

2335 = $\frac{7000}{1 + 6e^{-0.55t}}$

2335$(1 + 6e^{-0.55t})$ = 7000

$1 + 6e^{-0.55t}$ = $\frac{7000}{2335}$

$6e^{-0.55t}$ = $\frac{7000}{2335}-1$

$6e^{-0.55t}$ = $\frac{7000}{2335}-\frac{2335}{2335}$

$6e^{-0.55t}$ = $\frac{4665}{2335}$

$e^{-0.55t}$ = $\frac{4665}{2335(6)}$

$e^{-0.55t}$ = $\frac{1}{2}$

$lne^{-0.55t}$ = $ln\frac{1}{2}$

-0.55t = ln$\frac{1}{2}$

t = $\frac{ln\frac{1}{2}}{-0.55}$

t = 2

Year: 1980 + t   = 1980 + 2   = 1982