Question

These exercises use the radioactive decay model. The mass m(t) remaining after t days from a 40-g sample of thorium -234 is given by m(t)=40e^⁻⁰.⁰²⁷⁷ᵗ. After how long will only 10g of the sample remain?

Answer 1

To find out after how long only 10g of the sample remains, we can set up the equation m(t) = 10 and solve for t. After approximately 40.52 days, only 10g of the sample will remain.

Step-by-step explanation:

To find out after how long only 10g of the sample remains, we can set up the equation m(t) = 10 and solve for t. The equation for m(t) is given as m(t)=40e^(-0.0277t), where t represents time in days. Rearranging the equation, we have 10=40e^(-0.0277t).

To solve for t, we divide both sides of the equation by 40, giving us 0.25 = e^(-0.0277t). Taking the natural logarithm of both sides gives us ln(0.25) = -0.0277t. We can then solve for t by dividing both sides by -0.0277. Using a calculator, we find that t ≈ 40.52. Therefore, after approximately 40.52 days, only 10g of the sample will remain.