The initial value problem for Newton’s law of cooling is dT dt = −κ(T − T1), T(0) = T0 , where κ > 0 is constant and T1 is the constant ambient temperature. Solve the initial value problem to find how the temperature of the object evolves for t > 0.

According to a study conducted in 2015, 18% of shoppers said that they prefer to buy generic instead of name-brand products. suppose that in a recent sample of 1500 shoppers, 315 stated that they prefer to buy generic instead of name-brand products. at a 5% significance level, can you conclude that the proportion of all shoppers who currently prefer to buy generic instead of name-brand products is higher than .18? use both the p-value and the critical-value approaches.