ANSWER:
[tex]y=448e^{-0.693t}[/tex]
STEP-BY-STEP EXPLANATION:
An exponential function has the following form:
[tex]y=A\cdot e^{kt}[/tex]
Where A is the initial quantity, we can determine the value of k with a data point, just like this:
[tex]\begin{gathered} 56=448\cdot \:e^{k\cdot 3} \\ \\ \text{ we solve for k} \\ \\ e^{3k}=\frac{56}{448} \\ \\ \ln(e^{3k})=\ln\left(\frac{1}{8}\right) \\ \\ 3k=\ln\left(\frac{1}{8}\right) \\ \\ k=\frac{\ln\left(\frac{1}{8}\right)}{3} \\ \\ k=-0.693 \end{gathered}[/tex]
Therefore, the equation would be:
[tex]y=448\:e^{-0.693t}[/tex]
