MATH SOLVE

2 months ago

Q:
# MAJORRRR HElppp Plutonium-210 has a half-life of 140 days. Use the formula , where , is the remaining mass, is the original mass, and is the half-life, to determine how long it takes to reduce 300 milligrams of plutonium-210 to 200 milligrams.Arrange the steps in the right order to solve the problem.

Accepted Solution

A:

Answer:Step 1: Finding r using the formula ln 2/h[tex]1.\ r=\frac{ln\ 2}{h}\\ r=\frac{ln\ 2}{140}\\r=0.00495[/tex]Step 2: Substitute the values in given formula[tex]2.\ m_t=m_0e^{-rt}\\200=300e^{-0.00495t}[/tex]Step 3: Divide both sides by 300[tex]\frac{2}{3} =e^{-0.00495t}[/tex]Step 4: Take the natural logarithm on both sides[tex]ln\ \frac{2}{3} =ln\ e^{0.00495t}[/tex]Step 5: Simplify[tex]-0.405 = -0.00495t[/tex]Step 6: Divide both sides by 0.00495[tex]\frac{-0.405}{-0.00495} =t[/tex]Step 7: Simplify[tex]t=81.8\ days[/tex]