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MATH

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MATH

Category: Coursework

Subcategory: Mathematics

Level: College

Pages: 1

Words: 275

Name of Student
Name of Instructor
Course Code
Date of SubmissionMATH
Question 1
P=1-e-0.05t t – no. of days
To reach 75 %? 0.75=1-e-0.05te-0.05t=0.25-0.05t=ln0.25-0.05t=-1.386t=27.7 ≃28 days
Question 2
D=21% (0.79)t=xx0=2×0.79t=0.5tln0.79=ln0.5=ln0.50.79=2.94≃30 days
Question 3
People =1,000,000N t=1,000,0001-e-0.3tFor 800,000 to hear news
800,000=1,000,000 1-e-0.3t0.8=1-e-0.3te-0.3t=0.2-0.3t=ln0.2t=ln0.2-0.3=5.3 hrs
Question 4
wt=100(1-e-0.5t) t- weeks
80=100(1-e-0.5t)0.8=1-e-0.5te-0.5t=0.2-0.5t=ln0.2t=ln0.2-0.5=3.22 weeks
Question 5
fx=x2ln6xf’=2xln6x+x2.1x=2xln6x+xf”=2ln6x+2x1x+1=2ln6x+2+1=2ln6x+3fx=ln(x2+3)5f’=f’f=5(x2+3)4(2x)(x2+3)5=10x(x2+3)f”=10×2+3-2x10xx2+32=10×2+3-20x2x2+32c fx=e9xx2f’=9e9x(x2)-2xe9xx4f’=9x2e9x-2xe-9xx4f”=18xe9x+81x2e9x-(2e9x+18xe9x)x2d y=8e3x2-2y’=8(6xe3x2-2)=48xe3x2-2y”=48xe3x2-2+48x((6xe3x2-2)=48(1+6×2)e3x2-2(e)y =6ex8-5y’=6(12(x8-5)8x7ex8-5)=24×7(x8-5)ex8-5=24×7(x8-5)ex8-5y”=168×6(8×7-5)ex8-5(f)fx=x2lnx-17×7+ ex7+5f’=2xlnx+x2.1x-177×6+7x6ex7=2xlnx+1xx2-x6+7x6ex72xlnx+x-x6+7x6ex7 f”=2lnx+2x.1x+1-6×5+42x5ex7+7×6.7x6ex7f”=2lnx+2x.1x+1-6×5+42x5ex7+(7×6)2ex7=2lnx+3-6×5+42x5ex7+49x12ex7Question 6
Vt=11,000e-0.25tP=$11,000After 4 years
Vt=11,000e-0.25×4=4046.67Rate of change = 11,000-4046.6711,000×100%=63.2%Question 7
N=60,000 Nt=60,000(1-e-0.3t)After 5 hrs Ns=60,0001-e-0.3×5=46,612Rate of days will be 46,61260,000×100%=77.7%Question 8
Dp=75,00065-p p-price
Charges – 35 cents
Dp=75,00065-3…

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