When physicians prescribe medication, they must consider how the drug's effectiveness decreases over time. If, each hour, a drug is only 75% as effective as the previous hour, at some point the patient will not be receiving enough medication and must receive another dose. This situation can be modeled with a geometric sequence. (See the section on Geometric Sequences and Series.) If the initial dose was 190 mg and the drug was administered 3 hr ago, the expression 190(0.75)^2 represents the amount of effective medication still available. Thus, 190(0.75)^2=107 mg are still in the system. (The exponent is equal to the number of hours since the drug was administered, less one.) How long will it take for this initial dose to reach the dangerously low level of 60 mg?

During an epidemic, the number of people who have never had the disease and who are not immune (they are susceptible) decreases exponentially according to the following function, where t is time in days

f(t)=17,000e^−0.06t

Find the number of susceptible people at each time.

(a) at the beginning of the epidemic (b) after 6 days (b) after 3 weeks

An employee wants to invest $50,000 in a pension plan. One investment offers 6% compounded quarterly. Another offers 5.25% compounded continuously.

(a) Which investment will earn more interest in 4 yr?

(b) How much more will the better plan earn?