Precalculus Question

Question

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 In(t + 1).

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

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

Answer 1

a) D(15) = 91+160ln(15+1) ≈ 534 deaths

b) 600 = 91 + 160ln(t+1) --> ln(t+1) = (600-91)/160 = 3.18125

e^ln(t+1) = t+1 = e^3.18125 ≈ 24 --> t = 23 days

Checking: D(23) = 91+160ln(23+1) = 599.4886 ---> close enough