What is the tangent of v=60(1-e^{-0.2t}) ?

The tangent of v=60(1-e^{-0.2t}) is v=12e^{-0.2a_{0}}t+60(1-e^{-0.2a_{0}})-12e^{-0.2a_{0}}a_{0}

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tangent of v=60(1-e^{-0.2t})

tangent of

v = 60 (1 - e^{- 0.2 t})

v = 12 e^{- 0.2 a_{0}} t + 60 (1 - e^{- 0.2 a_{0}}) - 12 e^{- 0.2 a_{0}} a_{0}

Solution steps

Compute the tangent line to the general point

t = a_{0}

Find the tangent point:

(a_{0}, 60 (1 - e^{- 0.2 a_{0}}))

Find the slope of

v = 60 (1 - e^{- 0.2 t}) : \frac{d v}{d t} = 12 e^{- 0.2 t}

Compute the slope of

v = 60 (1 - e^{- 0.2 t})

t = a_{0} : m = 12 e^{- 0.2 a_{0}}

Find the line with slope m=

12 e^{- 0.2 a_{0}}

and passing through

(a_{0}, 60 (1 - e^{- 0.2 a_{0}})) : v = 12 e^{- 0.2 a_{0}} t + 60 (1 - e^{- 0.2 a_{0}}) - 12 e^{- 0.2 a_{0}} a_{0}

v = 12 e^{- 0.2 a_{0}} t + 60 (1 - e^{- 0.2 a_{0}}) - 12 e^{- 0.2 a_{0}} a_{0}

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What is the tangent of v=60(1-e^{-0.2t}) ?
The tangent of v=60(1-e^{-0.2t}) is v=12e^{-0.2a_{0}}t+60(1-e^{-0.2a_{0}})-12e^{-0.2a_{0}}a_{0}