7 2 points SPreCalc7 46022 This exercise uses the radioacti

7. + -2 points SPreCalc7 4.6.022. This exercise uses the radioactive decay model. After 3 days a sample of radon-222 has decayed to 58% of its original amount. (a) What is the half-life of radon-222? (Round your answer to two decimal places.) days (b) How long will it take the sample to decay to 10% of its original amount? (Round your answer to two decimal places.) days Need Help? Read it

Solution

A(t) =A (1/2)^t/h

42= 100 (1/2)^3/h

0.42= (1/2)^3/h

log 0.42= (3/h) log (0.5)

t=2.4 days

b. 90=100 (1/2)^t/2.4

0.9 =(1/2)^t/2.4

log 0.9 = (t/2.4) log (0.5)

t=0.36 days