I keep impeccable notes, and have kept all tests, quizes, lecture notes, and study guides for every class I have ever taken. I have even digitized them and keep them on my google drive. Anyways, was thinking the other day it would be sweet if I could start making good money by selling stuff I already have.
figured it out if f(x)=x^6 h(x) then, f'(x)=(x^6)' h(x) + h'(x) (x^6) -> f'(x)=6x^5 h(x) + h'(x) x^6 now plus in -1 for x f'(-1)=6(-1)^5 h(-1) + h'(-1) (-1)^6 -> (since we know the values for h(-1) and h'(-1)) f'(-1)=-6(5) + 8(1) -> f'(-1)= -30 +8 -> f'(-1)= -22
Comments
For 32, as t goes to infinity, e^-kt goes to 0 and you'll get 25+54 for the first part. For the second part, just set t = 0.
sorry i should have been more clear what those markings meant
Doubling period is 10 minutes, so 2Ae^(k*0) = Ae^(k*10) -> 2 = e^10k -> ln 2 = 10k -> k = (ln 2)/10
80000 = Ae^(100*k) -> A = 80000/e^(100*k), and you know k now. A is the initial population.
for the last part convert 5 hours to minutes and just plug it in now that you have k and A
it says thats not right
i wish my teacher had given us formulas or something for this
or showed us steps at least
7400 = 5000(1+.075/4)^(4t)
7400/5000 = (1+.075/4)^(4t)
ln(7400/5000) = 4t*ln(1+.075/4)
Solving for t is straightforward from there.
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I keep impeccable notes, and have kept all tests, quizes, lecture notes, and study guides for every class I have ever taken. I have even digitized them and keep them on my google drive. Anyways, was thinking the other day it would be sweet if I could start making good money by selling stuff I already have.
i had the /4 under the whole quantity 1+.075 instead of just the .075
just the steps since id like to try and solve it on my own
if f(x)=x^6 h(x) then, f'(x)=(x^6)' h(x) + h'(x) (x^6) -> f'(x)=6x^5 h(x) + h'(x) x^6
now plus in -1 for x
f'(-1)=6(-1)^5 h(-1) + h'(-1) (-1)^6 ->
(since we know the values for h(-1) and h'(-1))
f'(-1)=-6(5) + 8(1) -> f'(-1)= -30 +8 -> f'(-1)= -22