# Question It's a horror movie trope - someone goes on a cruise, but doesn't know that they are infected with a nasty virus. The cruise ship leaves port with 6000 people (including passengers and cruiseline workers). By the fifth day, a total of 28 people have been infected by the deadly virus. For the remainder of this problem, you may assume that the rate of virus spread is proportional to both the number of infected people $$P$$ and the number of people not infected. a. How manv deople have succumbed to the virus by day twelve? (Round down to the nearest person.) people b. How lone will it be until half of the ship's population is infected? (Round to the nearest day.) $$\boldsymbol{t}=\quad$$ days

Transcribed Image Text: It's a horror movie trope - someone goes on a cruise, but doesn't know that they are infected with a nasty virus. The cruise ship leaves port with 6000 people (including passengers and cruiseline workers). By the fifth day, a total of 28 people have been infected by the deadly virus. For the remainder of this problem, you may assume that the rate of virus spread is proportional to both the number of infected people $$P$$ and the number of people not infected. a. How manv deople have succumbed to the virus by day twelve? (Round down to the nearest person.) people b. How lone will it be until half of the ship's population is infected? (Round to the nearest day.) $$\boldsymbol{t}=\quad$$ days
Transcribed Image Text: It's a horror movie trope - someone goes on a cruise, but doesn't know that they are infected with a nasty virus. The cruise ship leaves port with 6000 people (including passengers and cruiseline workers). By the fifth day, a total of 28 people have been infected by the deadly virus. For the remainder of this problem, you may assume that the rate of virus spread is proportional to both the number of infected people $$P$$ and the number of people not infected. a. How manv deople have succumbed to the virus by day twelve? (Round down to the nearest person.) people b. How lone will it be until half of the ship's population is infected? (Round to the nearest day.) $$\boldsymbol{t}=\quad$$ days
&#12304;General guidance&#12305;The answer provided below has been developed in a clear step by step manner.Step1/2Solution:The cruise ship leaves port with 6000 people By the fifth day 28 people are infected by the deadly virus Let the exponential model is given by $$\mathrm{{P}{\left({t}\right)}={6{,}000}{e}^{{{r}{t}}}}$$at 5 days $$\mathrm{{5{,}972}={6{,}000}{e}^{{{5}{r}}}}$$$$\mathrm{{5}{r}={\ln{{\left(\frac{{28}}{{6{,}000}}\right)}}}}$$$$\mathrm{{r}=-{0.00093}}$$$$\mathrm{{P}{\left({t}\right)}={6{,}000}{e}^{{-{0.00093}{t}}}}$$(a) At ... See the full answer