   Chapter 11.3, Problem 61E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Radioactive decay The number of grams of radium, y, that will remain after t years if 100 grams existed originally can be found by using the equation -0 .000436 t = ln  ( y 100 ) Use implicit differentiation to find the rate of change of y with respect to t—that is, the rate at which the radium will decay.

To determine

To calculate: The rate at which the radium will decay if the number of grams of radium y that will remain after t years if 100 grams existed originally can be found by the use of the equation 0.000436t=ln(y100).

Explanation

Given Information:

The number of grams of radium y that will remain after t years if 100 grams existed originally can be found by the use of the equation, 0.000436t=ln(y100).

Formula used:

According to the chain rule, if f and g are differentiable functions with y=f(u) and u=g(x), then y is a differentiable function of x,

dydx=dydududx

Calculation:

As it is provided that the number of grams of radium y that will remain after t years if 100 grams existed originally can be found by the use of the equation:

0.000436t=ln(y100)

Now, the rate at which the radium will decay is given by dydt.

Now, differentiate both sides of equation with respect to t,

ddt(0

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