Story Problem!!!! 10 POINTS TO BEST ANSWER!!!

The very rigorous medical program at a local university has a 20% drop out rate for each year. If the school admits 1,000 freshmen, how many diplomas will need to be ordered 4 years later?

10 POINTS TO BEST ANSWER

This problem is exponential decay. It can be solved like this:

y=a(1-r)^t when a=original amount; r= rate of decay as a decimal; and t= time in years
y=1000(1-0.2)^t
y=1000(.8)^4
y=1000(0.4096)
y=409.6
The School will need to order 409 diplomas or 410 diplomas depending on if the .6 student dropped out or not.

Since there are 1,000 freshmen to begin with, and for each year 20% of the preceding year's number of students are dropped out, we can solve this using exponents:

1000 - 1000(0.20) - 1000(0.20)(0.20) - 1000(0.20)(0.20)(0.20) = 752

after first year 1000*.80= 800
2nd year 800*.8=640
3rd year 640*.8=512
4th year 512*.8= 409.6 or 410 or (0.8^4)1000

The actual equation would be {(1-0.2)^n}x

Where n is the number of years and x is the beginning enrollment

1st yr) +1000 - 200 = 800
2nd yr) +1000 +800 = 1800 -360 = 1440
3rd yr) +1000 +1440 = 2440 - 488 = 1952
4th yr) +1000 + 1952 = 2952 - 590 = 2362 diplomas

80% x 80% x 80% x 80%=.80*4=.4096

or about 410 diplomas are needed

1000x20/100=200 1000-200=800 diploma 800x20/100=160 800-160=640 640x20/100=128

640-128=512 ,

1st year: 800 left
2nd year: 640 Left
3rd year: 512 left
4th year: 410 Left

Around 410.

(80/100)^4 x 1000.

409.6 so I guess 410 ...