Question

Supongamos que el porcentaje R de personas que responden al anucio de un producto nuevo en un periodico y que lo compran despuest de t dias, viene dado por la siguiente formula: R=50-100*e^-0'3*t A) ¿Qué porcentaje de personas ha respondido y comprado después de 5 días? B)¿Cuántos días deben transcurrir para que el porcentaje que ha respondido y comprado sea el 40%?

Answer 1

A) R = 27.687

B) t = 8 days

Explanation:

(English question:

Suppose that the percentage R of people who respond to the advertisement of a new product in a newspaper and who buy it after t days, is given by the following formula: R = 50-100 * e ^ -0'3 * t A) What percentage of people have responded and bought after 5 days? B) How many days must elapse before the percentage that has responded and bought is 40%?)

A) To find the percentage of people that responded and bought after 5 days, we just need to use the value of t = 5 in the equation of R:

R = 50 - 100*e^(-0.3*5) = 50 - 22.313 = 27.687

B) To find how many days must elapse for the percentage to be 40%, we need to use the value of R = 40 and then find the value of t:

40 = 50 - 100*e^(-0.3*t)

-100*e^(-0.3*t) = -10

e^(-0.3*t) = 0.1

Using ln (natural logarithm) in both sides:

ln(e^(-0.3*t)) = ln(0.1)

-0.3*t = -2.3026

t = 7.6753 days

So after 8 days the percentage will be higher than 40%