How can i solve this problem?

Question

In many epidemics, the cumulative number of cases grows exponentially, at least over a limited time. A recent example is the spread of the Influenza A (H1N1) virus, commonly called the swine flu, which affected Mexico and the United States especially. On April 24, 2009, there were seven cumulative cases of swine flu in the United States reported to the World Health Organization. Over the next two weeks, the cumulative number of cases in the United States increased by about 40% each day. If this growth rate had continued, what would have been the cumulative number of cases in the United States reported 20 days after April 24? (Round your answer to the nearest whole number.)

cases

Answer 1

FV = Poe^rt where Po = original amount. FV = Future amount r=rate of increase per day, t=number of days, e = an irrational number = about 2.7. Use the formula for compound growth/decay, compounded continuously

at time t=0, Po =FV= 7

in 2 weeks, at time t =14, Po = 7, FV= 7(e^(.4)(14))

in 20 days, at time t=20, Po=7, FV = 7(e^(.4)(20))

= 7(e^8) = about 20,867 on May 14, 2009