Consider the geometric series S(x)=1+2(x−3)+4(x−3)^2+8(x−3)^3+⋯ Giving your answer as an interval, find all values of x for which the series converges.
Now assuming that x is in your interval above, find a simple formula for S(x).

Ariana starts with 100 milligrams of a radioactive substance. the amount of the substance decreases by 20% each week for a number of weeks, w. the expression 100(1−0.2)w finds the amount of radioactive substance remaining after w weeks. which statement about this expression is true? a) it is the difference between the initial amount and the percent decrease. b) it is the difference between the initial amount and the decay factor after w weeks. c) it is the initial amount raised to the decay factor after w weeks. d) it is the product of the initial amount and the decay factor after w weeks.