The first day Jenny went fishing, she caught exactly 31416 pounds of fish!
Even though she had more fish than she knew what to do with, she decided to go fishing again the next day. And she caught exactly 40% of what she caught the day before. Which was still a lot of fish.
She continued fishing every day. And every day she caught exactly 40% of what she caught the previous day.
If she continued fishing every day for twenty years, how many pounds of fish, total, would she catch? Please round to the nearest pound.
2007-05-26 07:02:53 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Geometric sequence.
a1=31416
r=.4
S7305=(31416(1-.4^7305))/(1-.4)
S7305=52360
Is the person in the source in your class?
2007-05-26 07:10:58 · answer #1 · answered by jsoos 3 · 1⤊ 1⤋
in 20 years there are 4 leap years
so the total number of days become
(16*365)+(4*366)=7304
the first day she caught 31416 pounds
the second day 31416 *40/100 ; 40% of total
the third day 31416 *40/100 *40/100 ;40% of the second day
and so on
this will give
31416 +31416 *40/100+31416 *(40/100)^2+31416 *(40/100)3+....... +31416 (40/100)^(7304-1)
this is a Geometrical progression
31416 (1+40/100+(40/100)^2+(40/100)^3+...+(40/100)^7303
now sum of n terms of GP = {a(1-r^n)}/(1-r)
a=1
r=40/100
n=7303
placing the corresponding values we get
= 1{1-(2/5)^7303}/1-(2/5)
=1/(3/5)=5/3
total pounds of fish caught in 20 years =31416 * 5/3=52360
that should be your answer or very close to it, whatever.
2007-05-26 14:34:10 · answer #2 · answered by $wap n!l 2 · 0⤊ 0⤋
52360 pounds of fish.
She actually has caught this much fish (rounded up) by day 13. The rest of the 20 years, she caught less than 0.5 pounds total.
2007-05-26 14:21:07 · answer #3 · answered by tom_2727 5 · 1⤊ 0⤋
Use a geometric sequence. Because it is a convergent series because r < 1, it should lead up to a number.
r= .4
t1=31416
Using these numbers and this equation:
t1 / 1-r
we can find how many pounds she caught!
31416 / (1-.4)
You get 52360 pounds of fish!!
2007-05-26 14:16:01 · answer #4 · answered by Anonymous · 1⤊ 0⤋
20 years is essentially infinite in this case so total is:
31,416* (1/(1-.4)) = 31,416/.6= 52,360 pounds.
If you want to be exact, 20 years = 20 *365.25 = 7305 days.
Then total = [(1-.4^7305)/(1-.4)]31,416 = 52,360 pounds.
There is an insignificant difference between 20 years and infinite years.
2007-05-26 14:37:10 · answer #5 · answered by ironduke8159 7 · 0⤊ 0⤋
This must be a popular homework assignment for teachers, given its frequent appearance in Yahoo Answers.
2007-05-26 14:13:09 · answer #6 · answered by Anonymous · 0⤊ 1⤋
u hav to use geometric progression.
ans is314126+314126*.4+314126*.4*.4. . ... .. . . .
314126{ 1(1-(0.4)^20*365-1)/1-0.4)}
2007-05-26 14:10:01 · answer #7 · answered by Ashwin 2 · 0⤊ 0⤋
The answer is 64,4340.
2007-05-26 14:13:07 · answer #8 · answered by Anonymous 3 · 0⤊ 3⤋