Element X decays radioactively with a half life of 5 minutes. If there are 340 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 4 grams?

32.0 min

Step-by-step explanation:

The equation that describes the decay of a radioactive isotope is:

(1)

where:

is the mass of the element at time t = 0

is the mass of the element left at time t

is the decay constant

The decay constant is related to the half-life of the element by

where

is the half-life

For element X, we have

So the decay constant is

We also know that for element X:

is the initial mass

is the final mass

So, from eq(1) we can now find the time:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

step-by-step explanation: the answer for wha if rt is 10 centimeters long, and wha is st? it’s 6