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Calculus/Intercepts and Slopes of exponential functions



I'm having a little trouble finding finding the intercept and slope of an exponential function. The function is y = 3.53*10^2 e^(2t^2)

My understanding is to get this in linear format the equation would turn into : ln(y)=ln(3.53x10^-2) + 2t^2

I have attached a graph of the function and can see that the curve intercepts y at around 3.52*10^-2 but cannot figure out why the solution to the slope according to the book equals 2.

I would really appreciate some help with this. Thanks in advance

The minimum of an exponential is where the exponent is minimal.
Since the exponent is x^2, the minimum of this is 0.

From this, it can be seen that the graph looks to be correct
and there is no intercept.

The slope is y', and that is y' = 353*e^(2t^2)(4t) = 1412t*e^(2t^2).
This would mean have a quickly increasing or decreasing slope
that quickly went to extremely high values on the right and
extremely small (large negative) on the left.


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