Susie went fishing one day and caught 31,416 pounds of fish!!! The next day she went again and caught exactly 40% of what she caught the day before.
For 20 years, Susie goes fishing every day, and every day she catches 40% of what she caught the previous day.
How many pounds of fish did susie catch in total....rounded to the nearest pound.
Thanks in advance.
2007-05-23 12:18:11 · 4 answers · asked by ms_upsidedown 4 in Science & Mathematics ➔ Mathematics
Day 1 ---- 31416 = a
r = 0.4
20 years ---- 365.25 days per year
20*365.25= 7305 days
n=7305
Sum of geometric series:
a(1-r^n)/(1-r)
=31416(1-0.4^7305)/(1-0.4)
0.4^7305 is of the order of 10^-2907. This is negligible and the series can be considered to be an infinite series.
Sum of infinite series = a/(1-r)
=31416/(1-0.4)
=31416/0.6
=52,360 pounds
2007-05-23 12:42:03 · answer #1 · answered by gudspeling 7 · 0⤊ 0⤋
Geometric series
a = 31416
r = 0.4
n = 20*365 = 7300
s_n = a(1 - (r^n)) / (1 - r)
s_20 = 31416(1 - (0.4^(7300)) / (1 - 0.4) = 52,360 pounds
2007-05-23 12:32:06 · answer #2 · answered by peateargryfin 5 · 1⤊ 0⤋
the fish she catches every day maks a GPwith first term a=31.416lband common ratior=0.6
20years=20*365=7300days. as these are many days, i regard the Gp as infinite.
the sum =a/1-r=31.416/0.478540lbs
2007-05-23 12:25:24 · answer #3 · answered by Anonymous · 0⤊ 3⤋
31,416(1.0010959^365*20)= 93,245,973 pounds
2007-05-23 12:28:22 · answer #4 · answered by ironduke8159 7 · 0⤊ 3⤋