Question

A model for the radioactive decay of 100 grams of Polonium -210 is m(t)=100e^(-1.807t), where m(t) is the mass of Polonium -210 (in grams) after t years. How many grams of Polonium are left after 1.5.

Answer 1

After 1.5 years, approximately 6.7 grams of Polonium-210 will remain.

Step-by-step explanation:

Certainly! Let's go through the calculation in more detail.

The given model for the radioactive decay of Polonium-210 is m(t)=100e−1.807t , where m(t) is the mass of Polonium-210 in grams after

t years.

To find the remaining mass after 1.5 years (t=1.5), substitute t=1.5 into the model:

m(1.5)=100e−1.807×1.5

Now, calculate the exponent:

−1.807×1.5=−2.7105

Substitute this back into the expression:

m(1.5)=100e−2.7105

Now, calculate the value of the exponential term:

e−2.7105 ≈ 0.067527347

Multiply this by 100:

m(1.5)≈100×0.067527347

m(1.5)≈6.7527347

So, after 1.5 years, approximately 6.75 grams of Polonium-210 are left.