Compare the doubling times found with the approximate and exact doubling time formulas. Then use the exact doubling time formula to answer the following question:
A family of 100 termites invades your house and grows at a rate of 20% per week. How many termites will be in your house after 1 year (52 weeks)?
2006-11-21 06:55:02 · 5 answers · asked by RITA 1 in Science & Mathematics ➔ Mathematics
P = Ae^rt
P = 100e^(.2*52)
P = 100 * 32824.21
P = 3282421
2006-11-21 07:44:40 · answer #1 · answered by bourqueno77 4 · 0⤊ 0⤋
I wouldn't know the "approximate" formula but the exact formula would be T(1+r)^w, where T is the number of termites, r is the weekly rate of growth, and w is the number of weeks.
So, 100(1+20%)^52 = 100(1.2)^52 = 1,310,463 termites at the end of the year and a holey house.
2006-11-21 15:46:31 · answer #2 · answered by Kyrix 6 · 0⤊ 0⤋
T=Toe^kw
T/To=1.2=e^k
ln 1.2=k
k=0.18232155679395462621171802515451
T/To=e^0.18232155679395462621171802515451*52
T/To=e^9.4807209532856405630093373080348
T/To=13104.630936003095673591722796493 times as many termites after 1 yr
Also can be found from T/To=1.2^52=13104.630936003095673591722796493
2006-11-21 16:30:18 · answer #3 · answered by yupchagee 7 · 0⤊ 0⤋
100(1+.2)^52
= 1310463.0936003095673591722796...
its compound interest
2006-11-21 15:58:55 · answer #4 · answered by Malvi 2 · 0⤊ 0⤋
100(1+.2)^52
= 1310463.0936003095673591722796493
compound interest!!!!!!!
2006-11-21 15:00:21 · answer #5 · answered by daldi 1 · 0⤊ 0⤋