If $y = e^{2 x + 5}$ then $y_{n} (0)$ equals

e^{5}

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2 (e^{5})

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e^{5} {.2}^{n}

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Solution

The correct option is C $e^{5} {.2}^{n}$
$y = e^{2 x + 5}$
$y_{1} = 2 e^{2 x + 5}$
$y_{2} = 2^{2} e^{2 x + 5}$
:
:
$y_{n} = 2^{n} e^{2 x + 5}$
Hence
$y_{n} (0) = 2^{n} e^{5}$ .

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