What is the limit as t approaches infinity of Q(t)+(100-Q(t))e^{-kt} ?

The limit as t approaches infinity of Q(t)+(100-Q(t))e^{-kt} is Undefined

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limit as t approaches infinity of Q(t)+(100-Q(t))e^{-kt}

t \to \infty lim (Q (t) + (100 - Q (t)) e^{- k t})

Undefined

Solution steps

t \to \infty lim (Q (t) + (100 - Q (t)) e^{- k t})

Q (t) + (100 - Q (t)) e^{- k t} = Q (t) (1 + \frac{( 100 - Q ( t ) ) e ^{- k t}}{Q ( t )})

= t \to \infty lim (Q (t) (1 + \frac{( 100 - Q ( t ) ) e ^{- k t}}{Q ( t )}))

Simplify

Q (t) (1 + \frac{( 100 - Q ( t ) ) e ^{- k t}}{Q ( t )}) : Q (t) + 100 e^{- t k} - e^{- t k} Q (t)

= t \to \infty lim (Q (t) + 100 e^{- t k} - e^{- t k} Q (t))

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

= t \to \infty lim (Q (t)) + t \to \infty lim (100 e^{- t k}) - t \to \infty lim (e^{- t k} Q (t))

t \to \infty lim (Q (t)) = Q (\infty)

t \to \infty lim (100 e^{- t k}) = 0

t \to \infty lim (e^{- t k} Q (t)) =

Undefined

= Q \cdot \infty + 0 - Undefined

= Undefined

What is the limit as t approaches infinity of Q(t)+(100-Q(t))e^{-kt} ?
The limit as t approaches infinity of Q(t)+(100-Q(t))e^{-kt} is Undefined