Arturo O. answered • 12/11/19

Experienced Physics Teacher for Physics Tutoring

P(t) = 210 / (1 + 25e^{-0.15t})

(a)

As t→∞, e^{-0.15t} → 0, so

P(t) → 210 / [1 + 25(0)] = 210

(b)

Set

P(t) = 116

and solve for t.

116 = 210 / (1 + 25e^{-0.15t})

1 + 25e^{-0.15t} = 210/116

25e^{-0.15t} = 210/116 - 1

e^{-0.15t} = (210/116 - 1)/25

-0.15t = ln[(210/116 - 1)/25]

t = ln[(210/116 - 1)/25] / (-0.15) days = ? days

You should be able to finish from here.