Forge welding is a process in which two pieces of steel are joined together by heating the pieces of steel and hammering them together.

1). Forge welding is a process in which two pieces of steel are joined together by heating the pieces of steel and hammering them together. A welder takes a piece of steel from a forge at 1600°F and places it on an anvil where the outdoor temperature is 50°F. The temperature of the steel T (in °F) can be modeled by T = 50 + 1550e−0.05t, where t is the time in minutes after the steel is removed from the forge.

a. What is the temperature of the steel after 5 minutes? Round to the nearest degree.

b. How long will it take for the steel to reach a temperature of 100°F so that it can be handled without heat protection? Round to the nearest tenth of a minute.

2). 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).

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?