Cobalt‑60 is subject to radioactive decay, and each year the amount present is reduced by 12.3%.
The amount of cobalt‑60 present is an exponential function of time in years. What is the base of this exponential function?
(Use decimal notation. Give your answer to three decimal places.)
The base of an exponential function can be calculated by dividing the value at one time by the value at another time, raised to the power of the ratio of the time intervals. In this case, we can use the fact that the amount of cobalt-60 is reduced by 12.3% each year, which means that the amount after one year is 0.877 times the amount at the beginning of the year (100% - 12.3% = 87.7%). Therefore, the base of the exponential function is:
base = (amount after one year) / (amount at beginning of year) = 0.877 / 1 = 0.877
Rounding to three decimal places, the base of the exponential function is 0.877.