SOLUTION: if a graph is created showing ln z against t for this : z= 2e^(4t) - what is the gradient, and how do I work it out - I am struggling with understanding a text book. Please note t

Question 894150: if a graph is created showing ln z against t for this : z= 2e^(4t) - what is the gradient, and how do I work it out - I am struggling with understanding a text book. Please note this is not the actual problem I need to solve - it is similar - I need to understand how to do this type of question.
I have tried to follow the text and thought the gradient was equal to the power when I multiply by base e and reverse the order etc then use the line equation y=mx+c. Please can you help.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
The gradient is the derivative of the function.
In this case,

The value of the tangent line to the function at any point is the value of the derivative at that point.
.
.
.
As an example, when ,,
So the equation of the tangent line is,

On the graph, and
.
.
.

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