Question

I need help with my homework PLEASE CHECK WORK WHEN DONEi need number 9

Answer 1

`y=448e^(-0.693t)`

Explanation:

An exponential function has the following form:

`y=A\cdot e^(kt)`

Where A is the initial quantity, we can determine the value of k with a data point, just like this:

`\begin{gathered} 56=448\cdot \:e^(k\cdot 3) \\ \\ \text{ we solve for k} \\ \\ e^(3k)=(56)/(448) \\ \\ \ln(e^(3k))=\ln\left((1)/(8)\right) \\ \\ 3k=\ln\left((1)/(8)\right) \\ \\ k=(\ln\left((1)/(8)\right))/(3) \\ \\ k=-0.693 \end{gathered}`

Therefore, the equation would be:

`y=448\:e^(-0.693t)`