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The point $P\,$ lies on the curve with equation

y = 4e^{2x+1}.

The $y$ -coordinate of $P\,$ is 8.

a.

Find, in terms of $ln⁡2\ln 2$ , the $x$ -coordinate of $P$ .

[2]

b.

Find the equation of the tangent to the curve at the point $P\,$ in the form $y = a x + b$ , where $a\,$ and $b\,$ are exact constants to be found.

[4]

Logs

The point $P\,$ lies on the curve with equation

y = 4e^{2x+1}.

The $y$ -coordinate of $P\,$ is 8.

a.

Find, in terms of $ln⁡2\ln 2$ , the $x$ -coordinate of $P$ .

[2]

b.

Find the equation of the tangent to the curve at the point $P\,$ in the form $y = a x + b$ , where $a\,$ and $b\,$ are exact constants to be found.

[4]

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