Mayelin Hernandez II.) Problems 8, 9 8.) Find all

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Mayelin Hernandez II.) Problems 8, 9 8.) Find all
Mayelin Hernandez II.) Problems 8, 9 8.) Find all solutions o the differential equation f1(x)=2f(x), f(10)=10. dy
= 2y dx
dy
= 2dx y
dy
= 2dx y
ln y = 2x + c y = e!"!! y = e!" e! 10 = e! !" !! ln 10 = 20 + c c = ln 10 − 20 y = e!" e!" !" !!" y = 10e!"!!" 9.) The amount of a radioactive substance remaining decreases at a rate proportional the amount of the substance. Give that A(0) = 100mg and A(10) = 90mg, at what time are there 50mg remaining? dA
= kA dt
dA
= kdt A
𝑑𝐴
=
𝐴
𝑘𝑑𝑡 ln|A|=kt+c A=ekt+c A t = e! ekt 100 = A 0 = ec A t = 100ekt 90=A 10 = 100ek(10) . 9 = e!(!") ln . 9 = k(10) 1n(.9)
= k 10
!" (.!)
A t = 100e !" (!) A t = 100 ∗ (0. 9)!/!" 50=A(t)=100*(0.9)t/10 . 5 = (0.9)!/!" t
ln . 5 = ln 0.9 ∗ 10
ln . 5 ∗ 10
10
t=
= ln −.4 ∗ 10 =
1n 0.9
1n(.4)

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