Solve the problem.
-A certain radioactive isotope decays at a rate of 2% per 100 years. If t represents time in years and y represents the amount of the isotope left then the equation for the situation is $$\mathrm { y } = \mathrm { y } 0 \mathrm { e } ^ { - 0.0002 \mathrm { t } }$$ In how many years will
There be 94% of the isotope left?
A) 300 yr
B) 256 yr
C) 600 yr
D) 309 yr

Question

Quizplus · Accepted Answer

Setting up the equation with 94% of the isotope left, we get:

0.94 = e^(-0.0002t)

Taking the natural logarithm of both sides, we get:

ln(0.94) = -0.0002t

Solving for t, we get:

t = - ln(0.94) / 0.0002

Using a calculator or logarithm table, we get:

t ≈ 308.5

Rounding up to the nearest whole number, we get:

t = 309

Therefore, the answer is D) 309 yr.

Solve the Problem y=y0e−0.0002t\mathrm { y } = \mathrm { y } 0 \mathrm { e } ^ { - 0.0002 \mathrm { t } }y=y0e−0.0002t

Solve the Problem $\mathrm { y } = \mathrm { y } 0 \mathrm { e } ^ { - 0.0002 \mathrm { t } }$