exponential model

Question

In the first six months of an outbreak in 2014, the total number of reported cases was increasing at a continuous rate of about 74% per month. There were about 100 cases as of April 1, 2014. Find an exponential model in form C(t) = Ae^rt

 for the number of cases t months after April 1, 2014. HINT [See Example 5.]

C(t) = _______

Use it to predict the number of cases as of October 1, 2014. (Round your answer to the nearest integer.)

_____ cases

Answer 1

C(t) = Ae^rt r=74% = 0.74

t= 6 months from April 1 to Oct 1,

A=100, e= an irrational number =about 2.718

C = case count in t months

C(6) = 100e^.74(6)

= 100e^4.44

= 100(84.7749)

C(6) = 8,477.49

= about 8,477 cases by Oct. 1st

which is the answer you probably want

with continuous compounding, which is nature's way

It might also help if you provided "Example 5"

ignore what follows. Just some relatively mindless math games:

or recalculate in years, where 6 months = 1/2 = t, r = annual rate of increase 1.74^12 -1 =26.75=2675%

C(1/2) = 100e^26.75(1/2)

C(1/2) = 100e^13.376

C(1/2) =100(644351.17

C(1/2) = 64,435,117 by Oct. 1

and in a couple years wipe out the world's population

compounded monthly is a little less,

but no reason to suspect that

unless somehow people come together into major

contact about once a month only, for super spreader day

C(t) = A(1+r/n)^nt where n=number of compounding periods per month, if t is measured in months

= 100(1.74)^6

= 2,775

or

after one month,

C= 100+ .74(100) = (1.74)(100) = 174

after two months

C(2)=(1.74)^2(100) = 302.76

three months

C(3)= (1.74)^3(100)

six months

C(6) = (1.74)^6(100) = 2775

C= about 2,775 by Oct. 1

or with no compounding at all

one month 174

2 months another 74, for 248

3 months 322

6 months 100+6(74)

= 100+444 = 544

If you want to scare people most

and cause major panic as much as possible,

go with the 2nd (mis)calculation which may also ignore

people's natural reactons to reduce the spread

using wrong units has led to major rocket science failures

with rockets missing their targets by endless miles

find the errors the above calculations and receive 2 points extra credit