Question

1. On August 31, 1854, an epidemic of cholera was discovered in London, England, resulting from a contaminated community water pump. By the end of September, more than 600 citizens who drank water from the pump had died. The cumulative number of deaths D(t) at a time t days after August 31 is given by D(t) = 91 + 160 ln(t + 1).

   1. Determine the cumulative number of deaths by September 15. Round to the nearest whole unit.

   2. Approximately how many days after August 31 did the cumulative number of deaths reach 600?

Answer 1

On August 31, 1854 the model is given by

D(t) = 91 + 160ln(t+1) , t is the days after August 31 , 1854

At september 15 , t=15

So D(15) = 91 + 160ln(15+1)

= 91+ 160ln(16)

= 535

So cumulative number of deaths by september 15 is 535 citizens.

When cumulative number of deaths reach to 600

Then from given model we have

600 = 91 + 160ln(t+1)

Or, 160ln(t+1) = 509

Or, ln(t+1) = 3.18125

Or, (t+1) = e^3.18125

Or, t+1 = 24

Or, t = 23

After 23 days of August 31 , the number of cumulative no of deaths will be 600.