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# Find an exponential function that fits the experimental data collected over time # Find an exponential function that fits the experimental data collected over time

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Modeling data distributions asked 2021-02-11

Find an exponential function that fits the experimental data collected over time t.

\begin{array}{|c|c|} \hline t & 0 & 1 & 2 & 3 & 4 \\ \hline y & 600.00 & 630.00 & 661.50 & 694.58 & 729.30 \\ \hline \end {array}

## Answers (1) 2021-02-12

Let the exponential function be, $$y=b(a)^{t}$$
$$\text{At}\ t=0$$
$$600=b(a)^{0}$$
$$b=600$$ And at $$t=1$$
$$630=600(a)^{1}$$
$$a=\ \frac{630}{600}$$
$$a=\ \frac{21}{20}$$ Therefore, the exponential function is $$y=600(\frac{21}{20})^{t}$$.

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