How do you integrate $f (t) = 1.4 e^{0.07 t}$ $f(t) = 1.4e^(0.07t)$ ?

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Answer 1 · 2017-10-23T15:35:06

$\int 1.4 e^{0.07 t} d o = 20 e^{0.07 t}$ $int 1.4e^(0.07t) do = 20 e^(0.07t)$

$f (t) = \int 1.4 e^{0.07 t} d t$ $f(t) = int 1.4e^(0.07t)dt$

$= (\frac{7}{5}) \int e^{\frac{7 t}{100}} d t$ $= (7/5) inte^((7t)/100) dt$

$u = \frac{7 t}{100}, d u = (\frac{7 t}{100}) d x, d x = (\frac{100}{7}) d u$ $u = (7t)/100, du = ((7t)/100)dx, dx = (100/7)du$

Apply constant multiple rule,

$f(t) = (cancel(7/5)cancel(100/7)) 20 int e^u du$

$f(t) = 20 int e^u du = 20e^u$

But $e^u = e^(0.07)$

$:. int 1.4 e^(0.07t) dt = 20 e^(0.07t)$

How do you integrate f(t) = 1.4e^(0.07t)f(t)=1.4e0.07tf(t) = 1.4e^(0.07t)?