Chapter 3, Problem 1RE

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

1. If P(t) = P₀e^0.15t gives the population in an environment at time t, then a differential equation satisfied by P(t) is __________.

To determine

To fill: the blank with appropriate answer to complete the given statement.

Answer to Problem 1RE

The complete statement is, “If $P\left(t\right)=P_0{e}^{0.15t}$ gives the population in an environment at time $t$, then a differential equation satisfied by $P\left(t\right)$ is $\underset{\_}{\frac{dP}{dt}=0.15P}$”.

Explanation of Solution

Given:

The given statement is , “If $P\left(t\right)=P_0{e}^{0.15t}$ gives the population in an environment at time $t$, then a differential equation satisfied by $P\left(t\right)$ is $\_\_\_\_\_\_\_\_\_$”.

Calculation:

Consider the population in an environment at a time $t$.

$P\left(t\right)=P_0{e}^{0.15t}$

Differentiate the above equation.

$\begin{array}{c}\frac{dP}{dt}=\left(0.15\right)P_0{e}^{0.15t}\\ =0.15P\end{array}$

Hence, the complete statement is, If $P\left(t\right)=P_0{e}^{0.15t}$ gives the population in an environment at time $t$, then a differential equation satisfied by $P\left(t\right)$ is $\underset{\_}{\frac{dP}{dt}=0.15P}$.