Oak wilt is a fungal disease that infects oak trees. Scientists have discovered that a single tree in a small forest is infected with oak wilt. They determined that they can use this exponential model to predict the number of trees that will be infected after t years.
f(t)=e^0.4t

Question:

Rewrite the exponential model as a logarithmic model that calculates the # of years, g(x) for the number of infected trees to reach a value of x.

The logarithmic model is:

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The original function is:

To find the inverse function, first, we exchange y and x, so:

Now, we have to isolate y, and we start applying the natural logarithm to both sides of the equality. So

Thus, the logarithmic model is:

A similar question is given at

Step-by-step explanation:

the logarithmic expression for an expression with e is called natural logaritm which is

this is written in the natural logarithm or ln bye removing the base e and replacing log by ln, as given in the above answer