A radioactive isotope is unstable and will decay by emitting a particle, transforming into another isotope. The assumption used to model such situations is that the amount of radioactive isotope decreases proportionally to the amount currently present. (a) Let N(t) designate the amount of the radioactive material present at time tt and let N0 = N(0). Write and solve the IVP for the radioactive decay of radioactive material. (b) The half-life of a radioactive material is the time required for it to reach one-half of the original amount. What is the half-life of a material that in one day decays from 12mg to 9mg?

The half life of substance A is 22 years, and substance B decays at a rate of 30 each decade. (a) Find a formula for a function f(t) that gives the amount of substance A, in milligrams, left after t years, given that the initial quantity was 100 milligrams. f(t) = help (formulas) (a) Find a formula for a function g(t) that gives the amount of substance B, in milligrams, left after t years, given that the initial quantity was 100 milligrams. g(t) help (formulas) (c) of which substance is there less in the long term? OA. There is less of substance B in the long term. OB. There is less of substance A in the long term. OC. There is no way to tell.

One of the main contaminants of a nuclear accident, such as that at Chernobyl, is strontium-90, which decays exponentially at a rate of approximately 2.4% per year. (a) Write the percent of strontium-90 remaining, P, as a function of years, t, since the nuclear accident. [Hint: 100% of the contaminant remains at t = 0.] P(t)= = (b) Estimate the half-life of strontium-90. NOTE: Round your answer to the nearest integer. The half-life of strontium-90 is (c) After the Chernobyl disaster, it was predicted that the region would not be safe for human habitation for 100 years. Estimate the percent of original strontium-90 remaining at this time. NOTE: Round your answer to the nearest integer. There is about of original strontium-90 remaining at this time. years. %

Carbon-14 is a radioactive element with a half-life of about 5,730 years. Carbon-14 is said to decay exponentially. The decay rate is 0.000121. We start with one gram of carbon-14. We are interested in the time (years) it takes to decay carbon-14. Find the amount (percent of one gram) of carbon-14 lasting less than 5,730 years. This means, find P(x > 5,730).