Long math problem!?

Question

Joe caught 31416lbs of fish one day. For the next 20 years (7300 days), Joe caught 40% of what he caught the day before from that starting day of 31416lbs. After 20 years, how many pounds of fish, total, would Joe have caught?

Answer 1

Well its an GP problem. (Geometric Progression)
Hope you know what it is.

Anyways to make it simpler:

First day catch = 31416 lbs
Second day catch = 40% of 31416 = 12566.4 lbs
Third day catch = 40% of 12566.4 = 5026.56 lbs

Now see the ratio of second day/first day = 0.4
Similarly third day/second day = 0.4
This pattern follows and hence forms a GP or geometric progression.

Let first term be 'a' and common ration be 'r'

a = 31416 lbs
r = 40/100 = 0.4

n = 7300 days

Sum of a GP = a(1-r^n)/(1-r)

= 31416(1 - 0.4^7300)/(1-0.4)

= 52360

Thus total lbs of fish Joe would have caught over the next 20 years = 52360 lbs

Answer 2

This problem involves a geometric series or geometric progression.

Let "a" be the first term of the series. Let r be the common ratio of the geometric series.

If a + (a)r + (a)r^2 + (a)r^3 + ..... + (a)r^(n -1) for n terms,

then the sum, S, of the series is

S = [a(1 - r^n)]/(1 - r)

In this case,

S = [31416( 1 - (0.4)^7300]/(1 - 0.4)

S = 52360

After 20 years, Joe caught 52,360 pounds of fish.

Answer 3

(Each day refers to the weight of fish caught on that day)
day 1 -> 31416
day 2 -> 40/100 * 31416 = 4/10 * 31416
day 3 -> (40/100) * 4/10*31416 (i.e 40/100 * day 2)
.
.
.
day n -> (4/10)^(n-1)*31416
(notice the choice of n and n-1 carefully...)

Here, n=7300
Using GP the summation of this is

31416 (1-(4/10)^7300)
----------------------------------
(1-4/10)

i.e
a*(1-r^(n))
------------------
(1-r)

Assuming the series is represented as
31416 ( 1+4/10+(4/10)^2 + .... + (4/10)^7299)

Since 7300 is a pretty huge number, you can neglect (4/10)^7300.
i.e (1-(4/10)^7300) ~ 0 (approximately zero)
(Effectively we are treating the series as an infinite Geometric Progression)

So, your answer is
31416/(1 - 4/10) = 31416*10/6
= 52360 lbs

Answer 4

AGAIN?? This is the 5th posting of this problem
in 1 week!!
Again, use a geometric progression to find the answer,
which is 52360 pounds of fish.

Answer 5

it's gonna be 80% so try 31416 times 80/100 =25132.8

Answer 6

"What kind of fish were they?"--Prof. Half*ss