On initial creation, one milligram of Remilium (the amount required for a single dose of the MILSA cure) produces 6,000 REM-waves. Remilium has a half-life of five years, meaning that every five years, the REM-waves decrease to half their previous amount. Based on current research, the safe level for REM-waves is 188 REM-waves.

Question

On initial creation, one milligram of Remilium (the amount required for a single dose of the MILSA cure) produces 6,000 REM-waves. Remilium has a half-life of five years, meaning that every five years, the REM-waves decrease to half their previous amount. Based on current research, the safe level for REM-waves is 188 REM-waves.
How long would it take Remilium to reach the safe level of 188 REM-waves?

GPT 3.5 · Answer

Using the information provided, we can calculate the number of REM-waves over time using the formula:

N = N0 * (1/2)^(t/T),

where:
N = final number of REM-waves (188 REM-waves)
N0 = initial number of REM-waves (6,000 REM-waves)
t = time elapsed
T = half-life of Remilium (5 years)

Plugging in the values, we get:

188 = 6,000 * (1/2)^(t/5)

Divide both sides by 6,000:

188/6,000 = (1/2)^(t/5)

0.03133 = (1/2)^(t/5)

Taking the natural logarithm of both sides to solve for t:

ln(0.03133) = ln((1/2)^(t/5))

ln(0.03133) = (t/5) * ln(1/2)

t = 5 * ln(0.03133) / ln(1/2)

t ≈ 27.44 years

Therefore, it would take approximately 27.44 years for Remilium to reach the safe level of 188 REM-waves.