Chapter 8.2, Problem 49HP

To determine

To write an equation that models the amount of substance decay.

Answer to Problem 49HP

  $△R=a(1-b^t)$

Explanation of Solution

Given:

Consider the case of radioactive substance. The amount of substance decays exponentially with time.

Calculation:

The amount of radioactive substance can be modeled by the following equation:

  $R=a{b}^t$

Where,

  $R$ Amount of radio-active substance

  $t=$ Time elapsed

  $a=$ Initial amount

  $b=$ Rat constant

Hence if initial and final amount is known, the difference would be:

  $\begin{array}{l}△R=R_1-R_2\\ =a-a{b}^t\\ △R=a(1-b^t)\end{array}$

Since change in amount $△R$ , initial amount a, and time elapsed t are already know, value of b can also be calculated from the above equation.