Chapter 7.4, Problem 27E

To determine

To Find: The exponential function $y=y_0{e}^{kt}$

Answer to Problem 27E

The exponential function $y=2e^{0.4581t}$

Explanation of Solution

Given information:

Graph

  

Calculation:

The exponential function $y=y_0{e}^{kt}$

Since $y_0=2$

  $y=2e^{kt}$ $\text{equation1}$

And

When $\text{t=2}$

  $\text{y=5}$

Putting the values of $y$ and $\text{t}$ in the $\text{equation1}$

  $\begin{array}{l}{\text{5=2e}}^{\text{2k}}\\ {\text{e}}^{\text{2k}}=\frac{5}{2}\\ 2k=\ln \left(\frac{5}{2}\right)\\ k=0.4581\end{array}$

Then $y=2e^{0.4581t}$