Question

Answer Problems 1 and 2 without referring back to the text. Fill in the blank or answer true or false.

1.If $\mathit{p}\left(\mathit{t}\right)={\mathit{p}}_0{\mathit{e}}^{0.15\mathit{t}}$gives the population in an environment at time t , then a differential equation satisfied by $\mathit{p}\left(\mathit{t}\right)$ is .

Short answer

The differential equation is$d/dtp\left(t\right)=0.15p\left(t\right)$

Step-by-step solution

Describe the given information

The given equation is$p\left(t\right)=p_0{e}^{0.15t}$ . To find the differential equation using its solution, the solution must be derivated and then must be substituted with the independent variable wherever it is required.

To solve the differential equation

Population in an environment at time is given by $p\left(t\right)=p_0{e}^{0.15t}$. Take the derivative of the given equation with respect to t.

Simplify further as,

Draw the conclusion

The differential equation for the given solution is$\frac{d}{dt}p\left(t\right)=0.15p\left(t\right)$ .