1.) Jeff's bank offers a savings account, compounded monthly, with an APR of 2.5%. If P = 3500 what is A(7)?

2.) Jeff's bank offers a savings account, compounded monthly, with an APR of 2.75%. If P = 2500, solve the equation A(t) = 5000 for t.

3.) Jeff's bank offers a savings account, compounded monthly, with an APR of 2.75%. What principal P should be invested so that the account balance is $3000 in three years?

4.)A radioactive isotope and its associated half-life are given. Assume that it decays according to the formula A(t) = A₀e^kt where A₀ is the initial amount of the material and k is the decay constant. Cobalt 60, used in food irradiation, initial amount 150 grams, half-life of 5.27 years, Find the decay constant k.

a.)Find a function which gives the amount of isotope A which remains after time t. A(t) =

b.)Determine how long it takes for 80% of the material to decay.

5.)A radioactive isotope and its associated half-life are given. Assume that it decays according to the formula . A(t) = A₀e^kt where A₀ is the initial amount of the material and k is the decay constant. Americium 241, used in smoke detectors, initial amount 0.62 micrograms, half-life of 432.7 years Find the decay constant k. Round your answer to four decimal places. k =

a.)Find a function which gives the amount of isotope A which remains after time t. A(t)=

b.)Determine how long it takes for 60% of the material to decay. Round your answer to two decimal places.

6.)A pork roast was taken out of a hardwood smoker when its internal temperature had reached 175F and it was allowed to rest in a 70F house for 30 minutes after which its internal temperature had dropped to 165F. Assume that the temperature of the roast follows Newton's Law of Cooling.

Newton's Law of Cooling (Warming): The temperature T of an object at time t is given by the formula

T(t) = T_a + (T₀ T_a)e^kt,

where T(0) = T₀ is the initial temperature of the object, T_a is the ambient temperature and k > 0 is the constant of proportionality which satisfies the equation (instantaneous rate of change of T(t) at time

t) = k (T(t) T_a).

(a) Express the temperature T as a function of time t in minutes.

T(t)	= (b) Find the time at which the roast would have dropped to 140F had it not been carved and eaten.