A quantity with an initial value of 980 decays exponentially at a rate of 0.3% every 6 decades. What is the value of the quantity after 49 decades, to the nearest hundredth?
The decay rate is 0.3% every 6 decades, which can be written as a decay factor of 1 - (0.3/100) = 0.997.
We can use the exponential growth/decay formula A = A_0 * (r)^n, where A is the final amount, A_0 is the initial amount, r is the decay factor, and n is the number of time periods.
In this case, A_0 = 980, r = 0.997, and n = 49. Substituting these values into the formula, we get:
A = 980 * (0.997)^49
Using a calculator to evaluate this expression, we find that A ≈ 977.11.
Therefore, the value of the quantity after 49 decades is approximately 977.11, to the nearest hundredth.