Question

Use the rule of 70 to estimate the time it will take an initial quantity to drop to half its value when h(x)=20*0.97^x, where x is months

Answer 1

The rule of 70 is used to estimate the time it will take an initial quantity to drop to half its value:
70 : (the decreasing rate) = x ( months )
The decreasing rate = 1 - 0.97 = 0.03 = 3%
x = 70 : 3 = 23.33 = 23 1/3 = 23 months and 10 days. 
Verify:
20 * 0.97^(23.33) = 9.83 ≈ 10