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Population-time, least squares method, exponential.

Exponential models are used more than linear models in population-time data modeling studies. (like \( P(t)=a c^{b t} \) ). Population-time data of a living species are shown below. Using the least squares method, find the values of \( a \) and \( b \) for the exponential function \( P(t)=a c^{b t} \) that best fits the above data. hint: \( \log _{a}(x \cdot y)=\log _{a}(x)+\log _{a}(y) \) \[ \begin{array}{l} \log _{a}\left(x^{y}\right)=y \log _{a}(x) \\ \log _{a}\left(a^{x}\right)=x \end{array} \]

y = a * c ^ x, which is not in the form of a linear equation. By taking the logarithm of both sides of the equation, we