Using an exponential function, it is found that it takes 18.6 days for 80% of the material to decay.
The amount of a substance after t days is modeled by:

In which:
- k is the decay rate, as a decimal.
- A(0) is the initial amount.
The half-life is of 8 days, hence
, and this is used to find k.







Hence:

The time it takes for 80% of the material to decay it t for which
, hence:






It takes 18.6 days for 80% of the material to decay.
To learn more about exponential functions, you can take a look at brainly.com/question/24906920
5% fail
so 100-5=95% are left
percent means parts out of 100
95% of 100 is

times 100=95
95 students are left assuming that the 5% that fail fail within 12 months
step 1
convert miles to km
1 mile is-----> 1.60934 km
18.5 miles/hour-----> 18.5*1.60934=29.77 km/hour
step 2
convert km/hour to km/minutes
29.77 km/hour--------> 29.77/60----> 0.4962 km/minutes
step 3
by proportion
0.4962 km/1 minutes=125 km/x minutes
0.4962 km----------> 1 minute
125 km-------------> x
x=125/0.4962----> x=251.91 minutes---------> x=251.9 minutes
the answer is
251.9 minutes
Alternative Method
step 1
convert km to miles
1 km is-----> 0.621371 miles
125 km-----> 125*0.621371--->77.67 miles
step 2
convert miles/hour to miles/minutes
18.5 km/hour--------> 18.5/60----> 0.3083 miles/minutes
step 3
by proportion
0.3083 miles/1 minutes=77.67 miles/x minutes
0.3083 miles----------> 1 minute
77.67 miles-------------> x
x=77.67/0.3083----> x=251.9 minutes